54 OP08 Abstracts

CP1

Improving Ultimate Convergence of An Aug-mented Lagrangian Method

Optimization methods that employ the classical Powell-Hestenes-Rockafellar Augmented Lagrangian are usefultools for solving Nonlinear Programming problems. Theirreputation decreased in the last ten years due to the com-parative success of Interior-Point Newtonian algorithms,which are asymptotically faster. In the present researcha combination of both approaches is evaluated. The ideais to produce a competitive method, being more robustand efficient than its ”pure” counterparts for critical prob-lems. Moreover, an additional hybrid algorithm is defined,in which the Interior Point method is replaced by the New-tonian resolution of a KKT system identified by the Aug-mented Lagrangian algorithm.

Ernesto G. BirginIME-USPDepartment of Computer Scienceegbirgin@ime.usp.br

Jose Mario MartinezUniversity of Campinasmartinez@ime.unicamp.br

CP1

Augmented Lagrangian Algorithm with RecursiveTrust-Region Method: Application to OptimalControl Problems with Equality Constraints

In this talk, preliminary numerical results of augmentedLagrangian algorithm ALDISCR by Sartenaer and Sachsare presented. This algorithm is tailored for infinite-dimensional optimization problems with equality con-straints, like optimal control problems. ALDISCR consid-ers a sequence of discretized augmented Lagrangian sub-problems with dynamically determined discretization levelsto ensure global convergence. An application of the recur-sive multiscale trust-region method from Gratton, Sarte-naer and Toint within this framework to solve the sub-problems is also proposed and discussed.

Romain DujolFacultes Universitaires Notre-Dame de la PaixDepartement de Mathematiquesromain.dujol@fundp.ac.be

Annick SartenaerUniversity of NamurDepartment of Mathematicsannick.sartenaer@fundp.ac.be

CP1

On the Use of Iterative Methods for Solving LinearEquations in Nonlinear Optimization

Solving linear equations is an important step in manymethods for nonlinear optimization, e.g., interior meth-ods. In some cases, the matrices are symmetric and ill-conditioned. This may be due to e.g. symmetrization ofthe linear equation in an interior method or ill-posedness ofan inverse problem. We discuss the behavior of conjugate-gradient type methods on such ill-conditioned linear equa-tions.

Anders Forsgren

Royal Institute of Technology (KTH)

Dept. of Mathematicsandersf@kth.se

CP1

A Second-Derivative SQP Method for Noncon-vex Optimization Problems with Inequality Con-straints

We consider a second-derivative �1 sequential quadraticprogramming trust-region method for large-scale nonlin-ear non-convex optimization problems with inequality con-straints. Trial steps are composed of two components; aCauchy globalization step and an SQP correction step. Asingle linear artificial constraint is incorporated that en-sures non-accent in the SQP correction step, thus ”guiding”the algorithm through areas of indefiniteness. A salientfeature of our approach is feasibility of all subproblems.

Daniel RobinsonOxford Universitydaniel.p.robinson@gmail.com

Nick GouldOxford UniversityRutherford Appleton Laboratorynick.gould@comlab.ox.ac.uk

CP2

A Multilevel Algorithm for Inverse Problems withBound Constraints

We present a provably scalable algorithm for solving a classof inverse problems in the presence of bound constraints.Previous analysis proved that the associated unconstrainedproblems can be solved efficiently using specially designedmultilevel preconditioners. An extension of that technol-ogy is combined with a semismooth Newton method toshow that the bound-constrained inverse problem can besolved at a cost that is decreasing with increasing resolu-tion relative to that of the forward problem.

Andrei DraganescuDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countydraga@math.umbc.edu

CP2

An Interior Method for Computing a Trust-RegionStep

We consider methods for large-scale unconstrained opti-mization based on finding an approximate solution of aquadratically constrained trust-region subproblem. Thesolver is based on sequential subspace minimization witha modified barrier ”accelerator” direction in the subspacebasis. The method is able to find solutions of the subprob-lem to any prescribed accuracy. Numerical results will bepresented. This is joint work with Philip Gill and JoshuaGriffin.

Jennifer ErwayDepartment of MathematicsWake Forest Universityerwayjb@wfu.edu

Philip E. GillUniversity of California, San DiegoDepartment of Mathematics

OP08 Abstracts 55

pgill@ucsd.edu

Joshua D. GriffinInformatics and Decision Sciences DepartmentSandia National Laboratoriesjgriffi@sandia.gov

CP2

Modified Line Search for High Dimensional Func-tions Optimization

This paper proposes a modified line search method whichmakes use of partial derivatives and re-starts the searchprocess after a given number of iterations by modifying theboundaries based on the best solution obtained at the pre-vious iterations. Performance of the proposed algorithm iscompared with genetic algorithm and particle swarm opti-mization for functions having up to 10,000 dimensions forwhich line search clearly outperforms the other methods.

Crina GrosanBabes-Bolyai Universitycrina.grosan@gmail.com

Ajith AbrahamNorwegian University of Science and Technologyajith.abraham@ieee.org

CP2

A Safeguarded Line Search Algorithm Using TrustRegion Approach

In this talk, we present an hybrid algorithm for uncon-strained nonlinear optimization which combines line searchand trust region strategies. More precisely, the proposedmethod implements a line search technique but allows theexploitation of directions of negative curvature by switch-ing to a trust region approach when such a direction is en-countered. We detail an adaptation of the Steihaug-Tointconjugate gradient algorithm and report some preliminarynumerical results.

Laetitia LegrainUniversity of NamurBelgiumlaetitia.legrain@fundp.ac.be

Annick SartenaerUniversity of NamurDepartment of Mathematicsannick.sartenaer@fundp.ac.be

CP2

Efficient Curve Detection Using the Gauss-NewtonMethod

The detection of geometric primitives, like lines, circles orellipses, in an image plays a crucial role in many com-puter vision applications. In this talk, we present a newapproach to such problem using a Low-Order-Value Opti-mization model that can be tackled by variations of theGauss-Newton method. The proposed model is robust tonoise and very efficient to find patterns described by manyparameters. We present extensive performance compar-isons to many classical algorithms.

Paulo J. S. SilvaUniversity of Sao Paulo

pjssilva@ime.usp.br

Roberto AndreaniDMA-IMECC-UNICAMPandreani@ime.unicamp.br

Giovane CesarUniversity of Campinasgiovane@ime.unicamp.br

Roberto Cesar JR.University of Sao Pauloroberto.cesar@vision.ime.usp.br

Mario MARTINEZUniversity of Campinasmartinez@ime.unicamp.br

CP3

Goal Oriented Adaptivity and Multilevel Tech-niques for Shape Optimization with Inviscid Flows

We present a continuous adjoint approach to shape opti-mization for turbulent flows modelled by the incompress-ible instationary Navier-Stokes equations.After introducing the analytical adjoint calculus in thepresence of stabilization terms, we will focus on adaptivitybased on a goal oriented error estimator and multilevel op-timization with inexact trust-region SQP techniques. Nu-merical results will be presented.

Christian BrandenburgTU DarmstadtGermanybrandenburg@mathematik.tu-darmstadt.de

Florian LindemannTechnical University of MunichGermanylindemann@ma.tum.de

Michael UlbrichTechnical University of MunichChair of Mathematical Optimizationmulbrich@ma.tum.de

Stefan UlbrichTechnische Universitaet DarmstadtFachbereich Mathematikulbrich@mathematik.tu-darmstadt.de

CP3

A Newton-Multigrid Method for One-Shot Pde-Constrained Optimization

We present a Newton-Multigrid method for the fast solu-tion of PDE-constrained optimization problems. Applyingan inexact Newton method to the nonlinear optimality sys-tem yields a sequence of quadratic optimization problems.An efficient preconditioner is mandatory for the coupled it-erative solution of these ill-conditioned and indefinite sys-tems. To this end, a multigrid algorithm together withappropriate smoothing iterations is developed. We discussdifferent relaxation methods and their properties for a va-riety of optimal control problems.

Martin EngelInstitute for Numerical Simulation

56 OP08 Abstracts

University of Bonn, Germanyengel@ins.uni-bonn.de

Michael GriebelUniversity of Bonn, Germanygriebel@ins.uni-bonn.de

CP3

The Minimization of an L∞-Functional Subject toan Elliptic PDE and Pointwise State Constraints

We study the optimal control of a maximum-norm ob-jective functional subjected to an elliptic-type PDE andpoint-wise state constraints. The problem is transformedto a problem where the on-differentiable L∞-norm in thefunctional will be replaced by a scalar variable and addi-tional state constraints. This problem is solved by barriermethods. We will show the existence and convergence ofthe central path for a class of barrier functions. Numericalexperiments complete the presentation.

Uwe PrufertTechnische Universitat Berlinpruefert@math.tu-berlin.de

CP3

Numerical Methods for Inverse Transport Prob-lems and Applications

We consider the problem of reconstructing physical param-eters (Σ(x) and Σs(x)) in the radiative transport equation:

θ · ∇u(x, θ) + Σ(x)u(x, θ) = Σs(x)∫Sd−1 k(θ · θ′)u(x, θ′)dμ(θ′)

u(x, θ) = g(x, θ), (x, θ) ∈ Γ−

where Γ− ≡ {(x, θ) ∈ ∂Ω×Sd−1 s.t. θ·ν(x) < 0}. Ω ∈ Rd

is the domain of interest and Sd−1 is the unit sphere inRd. We solve those inverse problems numerically using theframework of PDE-constrained optimization. Two specificapplications of those inverse problems are considered: opti-cal tomography and incoherent imaging in random media.Numerical examples based on synthetic and experimentaldata will be presented. Main references are: [1] Frequencydomain optical tomography based on the equation of ra-diative transfer, SIAM J. Sci. Comput., 28, 1463-1489,2006. [2] Transport-based imaging in random media, sub-mitted, 2007. [3] Experimental validation of a transport-based imaging method in highly scattering environments,Inverse Problems, 23, 2527-2539, 2007.

Kui RenUniversity of Chicagokren@uchicago.edu

CP3

PDE-Contrained Optimization in Nuclear ReactorDesigns.

In this study we will demonstrate how to use PDE-constrained optimization for nuclear reactor design. Theproblem is how to optimize the heat source such that thewall (clad) temperature will not exceed the melting tem-perature. Hence, it is inequality constrained optimization.Two approaches are proposed, i.e. inverse source and ex-terior penalty functional. Then, we compare the methodsto each other. Our conclusion is that the two techniquesare similar in terms of the optimized heat sources and the

temperatures.

Widodo SamyonoDept. of Appl. Phy, & Appl. Math., Columbia UniversityNew York, NYws2203@columbia.edu

David KeyesColumbia UniversityBrookhaven National Laboratorykd2112@columbia.edu

Dana A. KnollIdaho National LaboratoryDana.Knoll@inl.gov

CP4

Solution of Integer Bilevel Linear ProgrammingProblems

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Scott DenegreLehigh Universitysdenegre@lehigh.edu

CP4

An Optimization Approach to Radio ResourceManagement.

In this talk we consider a radio cellular system in whicheach cell manages the radio resources for its own usersand services. The radio resources are orthogonal withineach cell, e.g. Orthogonal Frequency Division Multiple Ac-cess (OFDMA). However, inter-cell interference is an issueif nearby cells use the same resorce simultaneously. Thescheduling problem of the system is posed as a mathemat-ical optimization problem. Various problem formulationsand different solution methods will be discussed.

Mikael P. Fallgren

Royal Institute of Technology (KTH)Optimization and Systems Theorywerty@kth.se

Anders ForsgrenRoyal Institute of Technology (KTH)Dept. of Mathematicsandersf@kth.se

CP4

A Two-Phase Approach for a Tramper ShipScheduling Problem

We present two-phase approach for solving a tramper shipscheduling problem in Japan. Firstly, a few transportationorders are aggregated into one order. Secondly, we solverouting problem by set partitioning approach. It involvesmany columns so that column-generation method is ap-plied. Because of the aggregation in the first-phase, thesubproblems become time-dependent shortest path prob-lems and are easily solved by labeling algorithm. Our nu-merical results show that the proposed algorithm is effec-

OP08 Abstracts 57

tive.

Kazuhiro KobayashiNational Maritime Research Institutekobayashi@nmri.go.jp

Mikio KuboTokyo University of Marine Science and Technologykubo@kaiyodai.ac.jp

Toshiyuki KanoNational Maritime Research Institutekano@nmri.go.jp

CP4

Discrete Bilevel Programming: Applications andSolution

A bilevel programming problem consists of an upper leveloptimization problem whose set of feasible solutions de-pends on the set of optimal solutions of a lower level prob-lem. Our focus is on discrete bilevel programming prob-lems where the lower and/or the upper level problems havebinary variables. We propose to reformulate the discreteproblem and solve it using a global optimization approach.Numerical results on a biofuel production application willbe presented.

Xiangrong LiuDrexel Universityxl35@drexel.edu

Hande Y. BensonDrexel UniversityDepartment of Decision Sciencesbenson@drexel.edu

CP5

Applications of Semidefinite Programs with Log-Determinant Terms

The Tsuchiya-Xia’s primal-dual path-following interior-point algorithm for SDPs with weighted log-determinantwas implemented in the SDPA. These problems often ap-pear in statistics related problems. We review the basicfeatures of Tsuchiya-Xia’s algorithm, and we present ap-plications in quantum tomography and data assimilationwhere we need to solve several small SDPs or a very largeSDP with weighted log-determinant.

Mituhiro FukudaTokyo Institute of TechnologyGlobal Edge Institutemituhiro@is.titech.ac.jp

CP5

Large Scale Semidefinite Programming Arisingfrom Chemistry

The electronic structure of ground state of atoms andmolecules are very important in chemistry and physics.The basic equation is Schroedinger equation, but it be-comes very hard to solve when the system becomes larger.We use the second-order reduced density matrix (2-RDM)as basic variable which is simpler, instead of complicatedwave function. This method is formulated as semidefiniteprogramming of arbitrary size. In this session, we present

some recent results of this method.

Maho NakataThe Institute of Physical and Chemical Researchmaho@riken.jp

CP5

New Sdp Relaxations for Quadratic AssignmentProblems Based on Matrix Splitting

QAPs are known to be among the hardest discrete opti-mization problems. In this talk we propose new SDP re-laxations for QAPs based on matrix splitting technique.Our new SDP relaxation has a smaller size compared withother SDP relaxations in the literature and can be solvedefficiently by most open source SDP solvers. Experimentsshow that rather strong bounds can be obtained for largescale QAP instances up to n=150. Further simplificationand improvement of our new model based on the datastructure in the underlying QAP will be discussed as well.

Jiming PengDepartment of Industrial and Enterprise SystemEngineeringUniversity of Illinois at Urbana-Champaignpengj@uiuc.edu

Hans MittlemannDepartment of Mathematics and StatisticsArizona State University,Tempe, AZ 85287-1804beck@plato.la.asu.edu

CP5

Matrix Convex Functions and Optimization

In this talk, we discuss various differentiation rules for gen-eral smooth matrix-valued functions, and for the class ofmatrix convex (or concave) functions first introduced byLowner and Kraus in the 1930s. For a matrix monotonefunction, we present formulas for its derivatives of any or-der in an integral form. Moreover, for a general smoothprimary matrix function, we derive a formula for all of itsderivatives by means of the divided differences of the orig-inal function. As applications, we use these differentiationrules and the matrix concave function logX to study a newnotion of weighted centers for Semidefinite Programming(SDP). We show that, with this definition, some knownproperties of weighted centers for linear programming canbe extended to SDP. We also show how the derivative for-mulas can be used in the implementation of barrier meth-ods for optimization problems involving nonlinear but con-vex matrix functions. This talk is based on a joint paperwith Jan Brinkhuis and Tom Luo.

Shuzhong ZhangThe Chinese University of Hong KongShatin, Hong Kongzhang@se.cuhk.edu.hk

CP6

Minimum Area Enclosing Ellipsoidal CylinderProblem

Given an arbitrary set A ∈ Rn and an integer k : 0 ≤k ≤ n, we are interested in finding an ellipsoidal cylin-der, centered at the origin, such that its intersection withthe subspace {y ∈ Rn : yk+1 = . . . = yn = 0} has mini-

58 OP08 Abstracts

mum area. This problem is referred to as the Minimum-Area Enclosing Ellipsoidal Cylinder (MAEC) problem. Weshow that MAEC and its dual can be written as convexproblems, and present a Frank-Wolfe type algorithm withaway steps. This algorithm finds an ε−approximate solu-tion in O(k(log k+ log logm+ ε−1)) iterations under someassumptions where |A| = m. We present some computa-tional results and discuss local convergence properties ofthe algorithm.

Damla Ahipasaoglu, Michael ToddCornell Universitydse8@cornell.edu, mjt7@cornell.edu

CP6

Dual Problems of Extremal Volume Ellipsoids

The minimum (maximum) volume ellipsoid containing(contained in) a convex body in Rn is an important prob-lem having applications in optimization, statistics, datamining and control theory, among others. As the numericalcomputation of these ellipsoids is needed in all the appli-cations mentioned, the study of the dual problems becomecrucial. In this talk, we focus on the duals of the extremalvolume ellipsoids utilizing semi-infinite programming dual-ity.

Filiz GurtunaGraduate studentgurtuna1@umbc.edu

CP6

A Simple Variant of the MTY-PC Algorithm andIts Objective-Function-Free Polynomial-Time Con-vergence for Bounded LPs

We analyze a simple variant of the Mizuno-Todd-Yepredictor-corrector (MTY-PC) algorithm for LP. The mod-ified algorithm utilizes a scaling-invariant two-layered leastsquares step which naturally arises when a scaling-invariantfinite termination procedure is considered. Under the as-sumption that the feasible region is bounded, we provepolynomial-time complexity of the algorithm that doesnot depend on the objective function. Our result yieldsa practical strongly polynomial-time complexity algorithmfor the feasibility problem of combinatorial LPs.

Tomonari KitaharaTokyo Institute of Technologykitahara.t.ab@m.titech.ac.jp

Takashi TsuchiyaThe Institute of Statistical Mathematicstsuchiya@sun312.ism.ac.jp

CP6

A Cutting Plane Method for Semi-Infinite LinearProgramming

We present a cutting plane algorithm for semi-infinite lin-ear programming. At each iteration a relaxation of theoriginal problem is formed that contains a finite numberof constraints. A point in the vicinity of the central pathof this problem is computed and violating constraints areidentified at this point. Then the relaxation is updated byadding the new constraints and the barrier parameter is si-multaneously reduced. We show that after a finite number

of iterations an ε-optimal solution is obtained.

Mohammad R. OskoorouchiCalifornia State University San Marcosmoskooro@csusm.edu

CP7

Smoothed Monte Carlo in Robustness Optimisa-tion

Robustness is seen as the probability mass of a design de-pendent set. An alternative for Monte Carlo is SmoothedMonte Carlo (SMC) estimation. The idea is to add asmoothing term to the MC estimation function resultinginto continuity in interesting design points. It is proventhat the resulting estimate function is continuous in suchpoints, arbitrarily close to the MC estimator and facilitatesthe use of standard optimisation algorithms. The whole isillustrated numerically.

Eligius HendrixWageningen UniversiteitUniversidad de Malagaeligius.hendrix@wur.nl

Niels OliemanRabobank Netherlandsniels.olieman@rabobank.com

CP7

A New Methodology for Evacuation ModellingAnalysis Using Numerical Optimisation Tech-niques

This work intends to demonstrate how optimization tech-niques can be applied to evacuation analysis to determineoptimal configurational layout. In particular we presenta methodology that combines the numerical techniques ofDesign of Experiments, Response Surface Models and nu-merical optimization with the buildingEXODUS evacua-tion simulation tool. The proposed methodology is demon-strated through an example involving a square room withtwo exits. The methodology is applied to this problem andthe optimal exit configuration is determined.

Rodrigo Machado TavaresOPTSEG - Optimal Safety Engineeringrodrigotmj@gmail.com

CP7

Pattern Search Algorithms for Circuit Design Op-timization

This research work presents three Pattern Search Algo-rithms, Mesh Adaptive Direct Search, Generalized PatternSearch and Particle Swarm Pattern Search, on two circuitdesign optimization problems: the parameter extraction ofan inductor circuit model and the problem of device sizingof an Operational Transconductance Amplifier. We com-pared these optimization algorithms in terms of quality androbustness of the solutions and in terms of the computa-tional effort needed to compute them.

Giuseppe NicosiaUniversity of CataniaDepartment of Mathematics & Computer Sciencenicosia@dmi.unict.it

OP08 Abstracts 59

Eva SciaccaMIT Massachusetts Institute of TechnologyDepartment of Mechanical Engineeringsciacca@mit.edu

CP7

Maximin Latin Hypercube Designs

Latin hypercube designs (LHDs) play an important rolein approximating computer simulation models. To ob-tain good space-filling properties, the maximin criterionis used, i.e., the objective is to obtain an LHD of n pointsin k dimensions with maximum separation (minimal) dis-tance. We give bounds for the separation distance of LHDsand give construction methods for approximate maximinLHDs. These results among others use mixed integer pro-gramming, a graph covering problem, and orthogonal ar-rays.

Edwin R. Van DamTilburg UniversityDept. Econometrics and Operations ResearchEdwin.vanDam@uvt.nl

CP7

A Method for Simulation Based Optimization Us-ing Radial Basis Functions

We propose an algorithm for the global optimization ofexpensive and noisy black box functions using responsesurfaces based on radial basis functions (RBFs). To han-dle noise, a method for RBF-based approximation is intro-duced. New points are selected to minimize the total modeluncertainty weighted against the surrogate function value.We present an extension of the algorithm to multiple ob-jectives. Numerical results on analytical test functions andsimulations show promise.

Adam WojciechowskiMathemal SciencesChalmers University of Technology, Gothenburg, Swedenwojcadam@chalmers.se

Michael PatrikssonMathematical Sciences,Chalmers University of Technologymipat@chalmers.se

Stefan JakobssonFraunhofer-Chalmers CentreGothenburg, Swedenstefan.jakobsson@fcc.chalmers.se

Johan RudholmChalmers Univeristy of Technologychm@etek.chalmers.se

CP8

Computing Optimal Trajectories for Low-EnergySpacecraft Transfers

The number of spacecraft missions in which low-thrustpropulsion systems are applied for orbit transfer and inter-planetary travel has been rapidly growing in recent years,because this technology has proven to enable missions thatwould otherwise not be feasible. The author will presenta number of examples of large trajectory problems relatedto low-energy and low-thrust transfers that have been op-

timized with NLP solvers.

Sven O. ErbEuropean Space Agencysven.erb@esa.int

CP8

Optimal Control of Delay Systems with Con-straints

We consider optimal control problems with constant de-lays in state and control variables under mixed control-state inequality constraints. First order necessary opti-mality conditions are presented and as well as a numeri-cal method based upon discretization techniques and non-linear programming. The theory and the proposed nu-merical method are illustrated by applications taken frombiomedicine and chemical engineering in order to apply theproposed algorithm and to compare the computed resultswith the theory.

Laurenz GoellmannMunster University of Applied Sciencesgoellmann@fh-muenster.de

Daniela KernWeierstrass Institute for Applied Analysis and StochasticsBerlin, Germanykern@wias-berlin.de

Helmut MaurerWest Wilhelms- Univ MunsterInst fur Num und Instr Mathmaurer@math.uni-muenster.de

CP8

On a Special Constraint in Least-Time Path Prob-lems.

We investigate a fairly general class of problems, that useconstraints related to prescribed speed. Related problemsarise naturally from considerations of conservation of en-ergy, as in the brachistochrone. No such assumptions areused here. The same equations for the parameter used todescribe the constraint, under a slight generalization, givesthat of curves of fixed rhumb. Based on similar ideas, wetry to provide the structure of a solution for the simplestof such constraints on a simple surface. We show a trivial,non-smooth solution, which might eventually be used inthe construction of a numerical solver.

Fabio GuerinoniDept of Mathematics and CSVirginia State Universityguerino@bit.csc.lsu.edu

CP8

Optimal Multi-Drug Control of a Delay-DifferentialModel of the Immune Response

Optimal control problems with time delays in state or con-trol variables and control-state inequality constraints arediscussed in the foregoing talk by Goellmann et al. Inthis talk, we apply the Minimum Principle and the nu-merical methods to the optimal control model of the im-mune response (R. Stengel et al., Optimal control of innateimmune response, OCAM 23, 91-104, 2002). Here, onlynon-delayed equations are considered, therapeutic agents

60 OP08 Abstracts

are treated separately and the objective function is as-sumed to be quadratic in control. In this talk, we discussoptimal multi-drug control protocols for non-delayed anddelayed equations and compare optimal solutions for ob-jective functionals of L2 and L1 type. Furthermore, wepresent state-constrained and time-optimal solutions. Weconsider optimal control problems with control appearinglinearly. This class of control problems is well studied forordinary differential equations. Here, the optimal controlis found to be a combination of bang-bang and singularsubarcs, where the junctions points between subarcs aredetermined by an associated switching function. The pur-pose of this talk to present several control problems forelliptic and parabolic equations which exhibit bang-bangand singular controls and illustrate phenomena similar tothose in the ODE case.

Helmut MaurerWest Wilhelms- Univ MunsterInst fur Num und Instr Mathmaurer@math.uni-muenster.de

CP8

On Convergence of Regularization Methods forParabolic Optimal Control Problems with Point-wise Control and State Constraints

Pointwise state constraints present a challenge for the anal-ysis as well as the numerical treatment of optimal con-trol problems, since associated Lagrange multipliers cangenerally only be expected to exist in the space of regu-lar Borel measures. In the past, different regularizationstrategies have been developed in order to avoid this dif-ficulty. They have, however, mainly been considered forpure state constraints or unilateral control and state con-straints. Here, we focus on semilinear parabolic optimalcontrol problems governed by bilateral pointwise state andcontrol constraints. Exemplarily, we apply Lavrentiev reg-ularization and present some difficulties associated with thegiven constraints. We rely on an additional assumption onthe structure of the problem, namely a separation conditionon the active sets, and show convergence for vanishing reg-ularization parameter as well as a local uniqueness resultfor local optima based on second order sufficient conditions.

Ira NeitzelTech University of BerlinDepartment of Mathematicsneitzel@math.tu-berlin.de

Fredi TroeltzschTech Univ of BerlinDepartment of Mathematicstroeltz@math.tu-berlin.de

CP9

Practical Methods for Constrained Oilfield Opti-mization

Oilfield optimization problems are expensive to computeand typically have constraints, possibly nonlinear, on thecontrol parameters. Such complex problems might nothave derivatives of the objective function available, becausethey are impossible to obtain analytically or too expensiveto evaluate numerically. Unfortunately, most derivative-free optimization algorithms treat unconstrained problems.In this study, we discuss the efficient use of penalty andlexicographic comparison based methods to optimize oil

production under nonlinear physical constraints.

Hugues Djikpesse, Benoit Couet, Michael PrangeSchlumberger-Doll ResearchHDjikpesse@slb.com, bcouet@boston.oilfield.slb.com,mprange@boston.oilfield.slb.com

William BaileySchlumberger-Doll Reaseachwbailey@boston.oilfield.slb.com

David WilkinsonEfficient Solutions Inc.davewilk@effisols.com

CP9

Systems of Systems Optimization Formulationswith Application to Aircraft Selection and Design

We examine optimization issues for systems of systems;these include the tradeoff of degree of central authorityvs. component autonomy, and predictive modeling of com-ponents input-output responses. We illustrate these opti-mization concepts on the problem of simultaneous productdesign and fleet mix optimization problem. Results will begiven for an aircraft selection exercise, including extensionto determining the best aircraft family, and to problemshaving a mix of continuous and categorical variables.

Paul D. FrankMathematics & Engineering AnalysisPhantom Works - The Boeing Companypaul.d.frank@boeing.com

Sharon Arroyo, Evin Cramer, John-Paul SabinoBoeingMath & Computingsharon.f.arroyo@boeing.com, evin.j.cramer@boeing.com,john-paul.n.sabino@boeing.com

CP9

Improving the Method of Seed Generation for aRoute Optimization Software Package

Quantm provides software for road and rail infrastructureplanning. A service Quantm provides is unseeded opti-mization, whereby 50 routes are produced from scratch,requiring the generation of 50 different seed routes from acontinuous space. The method for the generation of theseeds by constructing a network over the land surface andusing shortest path algorithms is presented, along with twodifferent attempts to improve the quality of results pro-duced by this method.

Liam Merlot, Peter GippsQuantm Ltdliam.merlot@quantm.net, peter.gipps@quantm.net

CP9

Optimization of Satellite Coverage

This project is concerned with satellite-based environmen-tal observation. For an effective monitoring of environmen-tal activities by a satellite, it is the main goal to achievemaximum coverage throughout a short period of time. Dueto technical restrictions of the satellite hardware, it is onlypossible to use the camera for a limited time period perorbit, while rotating around the Earth. The main goal is

OP08 Abstracts 61

to determine the time intervals for witch the coverage withrespect to given target areas is maximized and the restric-tions such as contact to ground stations are satisfied. Toachieve a continuous objective function for the sequentialquadratic programming method, the coverage is modelledby polygons integrated on a sphere. For acceptable com-puting times, special investigations had to be made in orderto achieve fast gradient computations.

Jan M. Tietjen, Christof Buskens, Matthias KnauerResearchgroup Optimization and Optimal ControlCenter of Industrial Mathematics in Bremenjtietjen@math.uni-bremen.de, bueskens@math.uni-bremen.de, knauer@math.uni-bremen.de

CP9

Forward Swept Wing Optimization by Using theGenetic Algorithm

This work is about forward swept wing (FSW) design prob-lem for reducing the optimization time and cost. Dynamicmesh technique was used in the design of a transonic FSWby coupling it with Genetic Algorithm. It is observed thatthe drag coefficient can be reduced by 15 percent whilethe lift coefficient close to the design value determined atthe beginning as a design constraint. The results are alsocompared to backward swept results.

Erguven VatandasAssist.Prof.Dr.e.vatandas@hho.edu.tr

CP10

Complexity Reduction of Calibration Problems inNumerical Finance

The pricing of derivatives has gained considerable impor-tance in the finance industry and leads to challenging prob-lems in numerical optimization. We focus on the numericalsolution of a stochastic model for option prices. In partic-ular, we are concerned with the calibration of these modelsto real data, which leads to large scale optimization prob-lems. We consider the numerical solution of these opti-mization problems and give some indication how to reducethe complexity of these problems.

Christoph KaebeUniversitaet Trier, Germanykaebe@uni-trier.de

CP10

Models and Algorithms for Stackelberg Gameswith Incomplete Information

Stackelberg games, where one player, the leader, selects itsaction first and the second player decides its optimal strat-egy knowing the actions of the leader is a natural problemfor various security domains. This framework however as-sumes the leader has an accurate model of the adversary.In this work we have developed efficient mixed-integer pro-grams and algorithms to solve situations where there is im-perfect information about the adversary, its reward struc-ture, or decision process.

Fernando OrdonezUSC, Industrial and Systems Engineeringfordon@usc.edu

CP10

A Numerical Method for Stochastic Control withApplications to Finance

We solve a series of stochastic control problems on a dif-fusion process using a combination of Ito calculus, martin-gale theory and linear programming. With sparse matrixtechniques, a manageable number of constraints and usingthe MOSEK solver embedded into Matlab, our methodol-ogy provides for a quick and easy way to solve this typeof stochastic control problem. We apply the numericalmethodology to a series of problems in corporate finance,yielding some interesting results.

Arnav ShethUC Berkeleyarnavsheth@gmail.com

Larry SheppRutgers Universityshepp@stat.rutgers.edu

Oded PalmonRutgers Business Schoolpalmon@rbs.rutgers.edu

CP10

Information Relaxations and Duality in StochasticDynamic Programs

We describe a dual approach to stochastic dynamic pro-gramming: we relax the constraint that the chosen pol-icy must be temporally feasible and impose a penalty thatpunishes violations of temporal feasibility. We describe thetheory underlying this dual approach and demonstrate itsuse in inventory models and option pricing models.

Peng Sun, David Brown, James SmithDuke Universitypsun@duke.edu, dbbrown@duke.edu, jes9@duke.edu

CP10

Index Policies for Discounted Bandit Problemswith Availability Constraints

We study a generalization of the multi-armed bandit prob-lem where arms are not always available. We prove thenon-existence of an optimal index policy and propose theso-called Whittle index policy by formulating the problemas a restless bandit problem. The index policy cannot bedominated uniformly by any other index policy over theentire class of bandit problems considered here, and is nu-merically shown to be near-optimal.

Kazutoshi Yamazaki, Savas Dayanik, Warren PowellPrinceton Universitykyamazak@gmail.com, sdayanik@princeton.edu,powell@princeton.edu

CP11

Globalization of Primal-Dual Methods for Nonlin-ear Programming

We propose a new globalization strategy for primal-dualmethods in nonlinear programming. Our technique relaxesthe usual requirement of solving the barrier problem witha precision of the same order as the barrier parameter.We show that the full Newton step is asymptotically ac-

62 OP08 Abstracts

cepted and that linear or superlinear convergence occurswhen the barrier parameter goes to zero linearly or super-linearly. Numerical experiments are presented.

Paul ArmandUniversite de LimogesLaboratoire XLIMpaul.armand@unilim.fr

Joel BenoistUniversite de Limogesjoel.benoist@unilim.fr

Dominique Orbancole Polytechnique de MontrealDepartment of Mathematics and Industrial Engineeringdominique.orban@polymtl.ca

CP11

A Graph-Based Decomposition Method forQuadratic Separable Programs

A graph is derived based on the QSP model. KKT comple-mentarity conditions are used in order to decide how thegraph has to be traversed in the solution process. Also,a decomposition strategy is applied in order to divide theproblem into subproblems by ”weakening” the links whichconnect the variables. This has the effect to take into ac-count those links to complete their gradient but are disre-garded in the propagation to solve the system.

Jaime Cerda Jacobo, David De RoureSchool of Electronics and Computer ScienceUniversity of Southamptonjcj03r@ecs.soton.ac.uk, dder@ecs.soton.ac.uk

CP11

Null-Space Primal-Dual Interior-Point Methodsfor Nonlinear Programs with Strong ConvergenceProperties

We consider a class of primal-dual interior-point methodsfor solving nonlinear optimization problems with generalinequality and equality constraints. The methods approx-imately solve a sequence of equality constrained barriersubproblems by computing a range-space step and a null-space step in every iteration. The �2 penalty function istaken as the merit function. Under very mild conditionson range-space steps and approximate Hessians, withoutassuming any regularity, it is proved that either all limitpoints of the iterate sequence are Karush-Kuhn-Tuckerpoints of the barrier subproblem and the penalty parame-ter remains bounded, or there exists a limit point that iseither an infeasible stationary point of minimizing the �2norm of violations of constraints of the original problemor a Fritz-John point of the original problem. Locally, weprove that by suitably controlling the exactness of range-space steps, selecting the barrier parameter and Hessianapproximation, the methods generate a superlinearly orquadratically convergent step.

Xin-Wei LiuDepartment of Applied Mathematics,Hebei University of Technologymathlxw@hebut.edu.cn

Ya-Xiang YuanChinese Academy of SciencesInst of Comp Math & Sci/Eng, AMSS

yyx@lsec.cc.ac.cn

CP11

Solving Continuous Nonlinear Optimization ViaConstraint Partitioning

We present a novel constraint-partitioning approach fornonlinear optimization. In contrast to previous work, ourapproach is based on a new exact penalty theory and canhandle global constraints. We employ a hyper-graph par-titioning method to recognize the problem structure. Weprove global convergence under assumptions that are muchmore relaxed than previous work and solve problems aslarge as 40,000 variables that other solvers such as IPOPTcannot solve.

You Xu, Yixin ChenWashington University in Saint Louisyouxu@wustl.edu, chen@cse.wustl.edu

CP12

On Automatic Differentiaton for Optimization

Automatic problem setup, e.g., by a modeling language,helps promote use of optimization algorithms. For somenonlinear optimization algorithms, accurate derivativecomputations are essential. This talk reviews use of auto-matic differentiation as an ingredient in optimization prob-lem setup, touching on implementation techniques, gradi-ent and Hessian-vector products, and experience both withfacilities connected with the AMPL modeling language andwith Sacado, a Sandia package for automatic differentiationof C++ codes.

David M. GaySandia National Labsdmgay@sandia.gov

CP12

Globally Convergent Three Term Conjugate Gra-dient Methods for Large-Scale Unconstrained Op-timization Problems

In this talk, we deal with a new three term conjugate gra-dient method for solving large-scale unconstrained opti-mization problems. It always generates sufficient descentdirection independently of line searches. We consider a suf-ficient condition for the global convergence of the proposedmethod within the line search strategy. Moreover, we pro-pose a new method within this strategy, and establish itsglobal convergence. Finally, some numerical results of theproposed method are given.

Yasushi Narushima, Hiroshi YabeTokyo University of ScienceDepartment of Mathematical Information Sciencenarusima@rs.kagu.tus.ac.jp, yabe@rs.kagu.tus.ac.jp

John A. FordUniversity of Essexfordj@essex.ac.uk

CP12

A Class of Methods Combining L-BFGS and Trun-cated Newton

We present a class of methods which is a combination ofthe limited memory BFGS method and the truncated New-

OP08 Abstracts 63

ton method. Each member of the class is defined by the(possibly dynamic) number of vector pairs of the L-BFGSmethod and a dynamic forcing sequence of the truncatedNewton method. We exemplify with a scheme which makesthe hybrid method perform like the L-BFGS method farfrom the solution, and like the truncated Newton methodclose to the solution. Numerical results indicate that thehybrid method usually performs well if one of its parentmethods performs well.

Trond Steihaug, Lennart FrimannslundUniversity of BergenDepartment of Informaticstrond@ii.uib.no, lennart@ii.uib.no

CP12

Limited Memory Bfgs Updating in a Trust-RegionFramework for Large-Scale Unconstrained Problem

In this talk we show that the limited memory updates tothe Hessian approximations can also be applied in the con-text of a trust-region algorithm. At each iteration, an ex-plicit quasi-Newton step is computed. If it is rejected, thenwe compute the solutions for trust-region subproblem withthe trust-region radius smaller than the length of quasi-Newton step. The key to this observation is the compactform of the limited memory updates derived by Byrd, No-cedal, and Schnabel. Numerical results will be discussed.

Liang Xu, James V. BurkeUniversity of Washingtonlxu@math.washington.edu, burke@math.washington.edu

Andreas WiegmannFraunhofer Institute for Industrial Mathematicsandreas@vicmasoft.com

CP12

Nonlinear Conjugate Gradient Methods withStructured Secant Condition for Nonlinear LeastSquares Problems

In this talk, we deal with conjugate gradient methodsfor solving nonlinear least squares problems. By combin-ing the idea of Dai-Liao’s conjugate gradient method andthe structured secant condition used in structured quasi-Newton methods, we propose conjugate gradient methodsthat make use of the structure of the Hessian of the ob-jective function. The present methods are shown to beglobally convergent under some assumptions. Finally, nu-merical results are reported.

Hiroshi YabeTokyo University of ScienceDepartment of Mathematical Information Scienceyabe@rs.kagu.tus.ac.jp

Michiya KobayashiTokyo University of ScienceGraduate School of Sciencej1106609@ed.kagu.tus.ac.jp

Yasushi NarushimaTokyo University of ScienceDepartment of Mathematical Information Sciencenarusima@rs.kagu.tus.ac.jp

CP13

Sensitivity to Observations in Model-ConstrainedOptimization

The sensitivity of the least-squares state estimation to ob-servational data is considered in the context of nonlinearmodel-constrained optimization. The sensitivity equationsare derived from the first order optimality conditions anda second order adjoint model is used to provide Hessianmatrix information. Practical implementation for large-scale systems and order reduction are discussed. Numer-ical results and sensitivity to time-space distributed dataare presented with a two-dimensional shallow-water model.

Dacian N. DaescuPortland State UniversityDepartment of Mathematics and Statisticsdaescu@pdx.edu

CP13

A Convex Output Least-Squares for the Elliptic In-verse Problems

The coefficients in a variety of linear elliptic partial differ-ential equations can be estimated from interior measure-ments of the solution. This talk will focus on the estimationof the coefficients in an abstract variational equation. Themain motivation behind the study of this inverse problemis to identify Lame coefficients in the system of linear elas-ticity. Recently, interesting applications, such as elasticityimaging, have sparked a new interest in this problem. Morespecifically, it is possible, using ultrasound, to measure in-terior displacements in human tissue (for example, breasttissue). Since cancerous tumors differ markedly in theirelastic properties from healthy tissue, it may be possible todiscover and locate tumors by solving an inverse problemfor the Lame parameters. Recently, we introduced a newmodified output least-squares formulation in an abstractsetting and proved its convexity. This circumvents a seri-ous deficiency of classical output least-squares functionalof being nonconvex in general. The abstract formulation isgeneral enough to be able to recover the main features ofthe total variation regularization. (The use of total vari-ation regularization allows the identification of discontin-uous coefficients.) The main emphasis of the talk will beon the stability issues for the modified output least-squaresfunctional. Two kinds of stability results will be presented.The first approach relies on a certain embedding propertiesof the spaces involved along with some functional analyticmanipulation of the functional. The second approach willmake use of some abstract results from optimization the-ory. Several numerical examples will presented to show thefeasibility of the approach.

Akhtar A. KhanNorthern Michigan Universityakhan@nmu.edu

Mark GockenbachMichigan Technological Universitymsgocken@mtu.edu

Baasansuren JadambaN/Ajadamba@mtu.edu

CP13

Constrained Orthogonal Distance Regression toCompute Parameters in a Lotka-Volterra System

64 OP08 Abstracts

of Differential Equations

We present an application which is modeled as a systemof differential equations. A finite number of values for thecurves that solve the system are available. The target isto compute parameters on the system in order to obtaincurves that are as close as possible to the observed data.Since the observed data may have noise in the primal vari-able, we propose an orthogonal distance regression schemeto compute such parameters.

Zeferino ParadaInstituto Tecnologico Autonomo de MexicoCol San Juan Xalpazeferino@gauss.rhon.itam.mx

Daniela BravoInstituto Tecnologico Autonomo de Mexicodanielabravo@hotmail.com

Georgina PulidoUniversidad Autonomo Metropolitana-Azcapotzalcogpr@correo.azc.uam.mx

Maria TriguerosInstituto Tecnologico Autonomo de Mexicotrigue@itam.mx

CP13

Parameter Identification with a Blood Pressure,Blood Flow Model

We present a compartmental model for blood pressure andblood flow in the human body. The resulting ODE systemcontains many physiological parameters specific to the sub-ject that are difficult to measure directly. We apply cuttingedge optimization techniques to identify parameter valuesthat cause the ODE solution to fit data collected nonin-vasively. Care is taken to determine the subset of modelparameters that can be identified reliably.

Scott R. PopeNorth Carolina State Universitysrpope@ncsu.edu

Tim KelleyNorth Carolina State UnivDepartment of Mathematicstim kelley@ncsu.edu

Mette OlufsenNorth Carolina State UniversityDepartment of Mathematicsmsolufse@ncsu.edu

Laura M. Ellwein, Cheryl ZapataNorth Carolina State Universitylmellwei@ncsu.edu, clzapata@ncsu.edu

CP14

Algorithms for Robust Shortest Path Problem

In the context of robust discrete optimization where datauncertainty is modeled by values belonging to closed in-tervals, the Bertsimas and Sim approach and the minimaxregret model are the main known methodologies. We im-plemented algorithms for solving robust shortest path innetworks instances using the two methodologies mentioned.

Interesting results were obtained when we analyzed exactand approximate solutions and the possible comparison forthese models.

Eduardo A. Alvarez-MirandaUniversidad de Talca, Merced 437eduardo.alvmir@gmail.com

Alfredo Candia-Vejar, Julio MardonesUniversidad de Talca, Merced 437Curico, Chileacandia@utalca.cl, jmardonescco@hotmail.com

CP14

Throughput Optimization in Mobile BackboneNetworks

This work develops techniques for throughput optimizationin a hierarchical distributed sensing architecture known asa mobile backbone network. We develop a novel techniquebased on mixed integer linear programming, which leads toa dramatic reduction in computation time compared to ex-isting optimal algorithms. Furthermore, we describe a newpolynomial-time approximate solution to this problem. Wealso formulate natural extensions to the mobile backbonenetwork problem and describe exact and approximate so-lutions for these extensions.

Emily CraparoDepartment of Aeronautics and AstronauticsMassachusetts Institute of Technologyemilyc@mit.edu

Jonathan P. HowMassachusetts Institute of TechnologyAerospace Controls Laboratoryjhow@mit.edu

Eytan ModianoDepartment of Aeronautics and AstronauticsMassachusetts Institute of Technologymodiano@mit.edu

CP14

Fully Polynomial Time Approximation Schemesfor Time-Cost Tradeoff Problems in Series-ParallelProject Networks

We consider the deadline problem and budget problem ofthe nonlinear time-cost tradeoff project scheduling modelin a series-parallel activity network. We develop fully poly-nomial time approximation schemes for both problems us-ing K-approximation sets and functions, together with se-ries and parallel reductions.

Chung-Lun LiThe Hong Kong Polytechnic Universitylgtclli@polyu.edu.hk

Nir HalmanMassachusetts Institute of Technologyhalman@mit.edu

CP14

Separable Spanning Trees Optimization for Com-munication Networks Reliability

This paper presents a class of iterative parametric dynamic

OP08 Abstracts 65

programming models devoted to networks reliability. Mul-tiobjective optimization is invoked as a separation strategyand the optimal solution is obtained by a multilevel strat-egy. Lower level weighted power Lagrangian problem issolved using dynamic programming. Upper level adjuststhe value of the weighting vector in the weighted powerLagrangian problem. The solution process is iterated untilthe optimal solution of the reliability optimization problemis found.

Alexandru MurguIIASmurgu@btinternet.com

CP14

Integer Programming for Optimization of a LargeTransportation Network

Given a set of processing centers, flows of resources, andthe existing multimodal transport network, we aim to op-timize the resource delivery in the terms of time, cost, andthe number of transshipping. The restrictions may concerntimes of delivery, predefine delivery routes and vehicles tobe used. We describe an integer programming approachto this problem and present some techniques for size re-duction. Computation on the transportation network ofRussia will be reported.

Sergey A. Yurkevich, Igor Isametdinov, AlexeyMartyushevRamax Internationalsergey.yurkevich@ramax.ru, igor.isametdinov@ramax.ru,alexey.martyushev@ramax.ru

CP15

A New Conic Solver for a Class of Structured Con-vex Problems

We present a new conic solver based on interior-point meth-ods that can solve a large class of convex problems, in par-ticular convex problems involving powers, exponentials andlogarithms, and report numerical results. We also presenta preliminary modelling environment suitable for formu-lating and feeding problems to this solver. A given convexproblem is transformed - if possible - into a structured conicformat based on the one-parameter family of power cones(including its limit).

Robert CharesUniversite catholique de LouvainCORErobert.chares@uclouvain.be

CP15

A Symmetric Primal-Dual Algorithm for ConicOptimization Based on the Power Cone

The power cones form a family of convex cones that al-low the formulation of a large class of convex problems(including linear, quadratic, entropy, sum-of-norm and ge-ometric optimization) into a unified structured conic for-mat. We introduce a primal-dual interior-point algorithmfor the this class of problems, which focuses on preservingthe perfect symmetry between the primal and dual sidesof the problem (arising from the self-duality of the powercone).

Francois GlineurUniversite Catholique de Louvain (UCL)

Center for Operations Research and Econometrics(CORE)francois.glineur@uclouvain.be

CP15

Fine Tuning Nesterov’s Optimal Descent Method

Each iteration of Nesterov’s algorithm for minimizing aconvex C1 function starts by computing a constant αk de-pendent on a Lipschitz constant L for f ′(·). Then a pointyk is computed, from which a steepest descent step deter-mines the next iterate xk+1. We modify the process by firstcomputing yk and xk+1 independent of L, and then an “op-timal” value of αk. The complexity obtained by Nesterovis kept and the performance improves in test problems.

Clovis C. GonzagaFederal Univ of Sta Catarinaclovis@mtm.ufsc.br

Elizabeth KarasFederal Univ. of Parana, BrazilDep. Matematica - UFPRkaras@mat.ufpr.br

CP15

An Improved VU-Algorithm for Partly SmoothMinimization

A recent VU-algorithm for mininimizing convex functionsimplictly exploits any underlying partly smooth functionstructure. It follows a ”primal-dual track” superlinearly,by alternating U-Newton-predictor-steps with V-corrector-steps. A prox-parameter-dependent bundle subroutineconstructs a V-model of the function using past subgra-dients in order to generate the required U-gradients. Thistalk describes an improved version that preserves globalconvergence while incorporating a new strategy for prox-parameter variation which allows this parameter to growwithout bound. Results of numerical experiments are pre-sented for validation.

Robert MifflinWashington State Universitymifflin@math.wsu.edu

Claudia A. SagastizabalIMPAsagastiz@impa.br

CP15

Distance Function and Infeasible-Start Interior-Point Method

We formulate the convex program into a unconstrainedproblem and solve by an infeasible-start interior-pointmethod. The method can be started from any interior-point. We give a new distance function which can be usedto study complexity of the method for feasible and infeasi-ble cases. We also give rounding error analysis and designan accurate numerical method for the method. Numericalexamples are provides.

Yurii NesterovCOREUniversite catholique de Louvainyurii.nesterov@uclouvain.be

66 OP08 Abstracts

Yu XiaSchool of MathematicsUniversity of Birminghamxiay@maths.bham.ac.uk

CP16

Variational Analysis of Robust Regularization

In continuous optimization, a solution can fail to be robustdue to inaccuracies in measurement and implementation.To address robustness in a minimization problem, we con-sider the maximum of a function over a bounded set andits translations over the domain. This method has regu-larizing properties, especially for semi-algebraic functions.The relationship between calmness and Lipschitz continu-ity in Variational Analysis generalizes robust regularizationto set-valued maps as well.

Chin How Jeffre PangCenter for Applied MathematicsCornell Universitycp229@cornell.edu

Adrian LewisCornell UniversityOper. Res. and Indust. Eng.aslewis@orie.cornell.edu

CP16

Stability Assessment of Partially Identified SystemUsing LMI Optimization

Vinnicombe Generalized Stability Margin (GSM) providespowerful tool for robustness assessment of control systemstability. However, it requires frequency response estima-tion of both the plant and controller of the system. Amethod is proposed for computation of GSM using only fre-quency response of joint“plant-controller” or “controller-plant” block. If the number of system inputs greatly exceedthe number of outputs or vice versa, the method allows toreduce expenses spent on system identification.

Serge L. ShishkinUnited Technologies Corp., Research Centershishks@utrc.utc.com

CP16

Robust Optimization and Problem Robustness

Robust Optimization has been an important approach inrecent years, with several emerging applications. Robustsolutions are protected from data variation, but the changein the robust solution with respect to the nominal solutionis related to the robustness and well posedness of the modelitself. In this work we show some results relating bothconcepts as well as some studies on simulated problem aswell as some real Supply Chain Management problems.

Jorge R. VeraPontificia Universidad Catolica de Chilejvera@ing.puc.cl

CP17

Reliability Optimization of Communication Net-works Using Genetic Algorithm

Evolutionary algorithms often have to solve optimizationproblems in the presence of a wide range of uncertainties.

A new genetic model is considered to study the reliabil-ity optimization in a linear consecutively connected sys-tem(LMCCS) by allocating multi state elements. A LM-CCS consists of (N+1) linear ordered positions. M statisti-cally independent multi state elements with different char-acteristics are to be allocated to the first N positions. Eachelement can provide a connection between the position towhich it is allocated and next few positions. The system isreliable if the first position (source) is connected with the(N+1)th position (sink) by means of suitable allocation ofthe multi state elements in various in between positions(workstations). This means that the signal can be trans-mitted with out interruption from the source to the sink.As further extension in the proposed genetic model, relia-bility optimization is attempted in LMCCS by allocatingMulti-state Elements in various workstations by consider-ing the adverse effects of noise in signal transmission. Thereliability of LMCCS is obtained using Universal Generat-ing Function technique. The optimal allocation is obtainedby means of Genetic Algorithm. For the one-to-one allo-cation problem, when the permutation crossover is used, itreduces the complexity of the problem and also yield betterresult compared to all the existing results.

Arulmozhi GanapathyDepartment of Mathematics & Computer application,PSG College of Technologyarul nithya2000@yahoo.com

CP17

Optimization Population-Based Algorithms forHigh-Performance Analog Circuits

This paper tackles the Integrated Circuit (IC) design bypopulation-based algorithms. The following real-life cir-cuits, RF Low Noise Amplifier, Leapfrog Filter, and UltraWideband LNA, were selected as test bed. The proposedalgorithms, Advaced-NSGAII and optIA, were shown toproduce acceptable and robust solutions in the tested ap-plications, where state-of-art algorithms, circuit designersand commercial techniques failed. The results show signif-icant improvement in all the chosen IC design problems.

Giuseppe NicosiaUniversity of CataniaDepartment of Mathematics & Computer Sciencenicosia@dmi.unict.it

Salvatore RinaudoST MicroelectronicsCAD Groupsalvatore.rinaudo@st.com

CP17

Automatic Layout Optimization of Power MosfetsUsing An Effective Population-Based Algorithm

The robustness of high-voltage discrete power MOSFETsstrictly depends on the topology of the layout device; theoptimization task is to minimize the maximum tempera-ture reached by the device. A complete exploration of thesolution space is impossible due the huge number of con-figurations. The designed population-based algorithm isable to find sub-optimal topologies, that improves the per-formance of the device of 27% respect the one proposedby designers and significantly outperforms state-of-art op-timization algorithms.

Giuseppe Nicosia

OP08 Abstracts 67

University of CataniaDepartment of Mathematics & Computer Sciencenicosia@dmi.unict.it

Franco Fiorante, Giuseppe GrecoST Microelectronicsfranco.fiorante@st.com, giuseppe-cad.greco@st.com

Salvatore RinaudoST MicroelectronicsCAD Groupsalvatore.rinaudo@st.com

Giovanni StracquadanioUniversity of CataniaDepartment of Mathematics and Computer Sciencestracquadanio@dmi.unict.it

CP17

Heuristically Evolving Populations Broaden Prob-lem Understanding

Population–based evolutionary heuristics can seek “decentsolutions” to challenging constrained optimization prob-lems when standard techniques do not yield optimal re-sults. Such problems are often only tentatively formulated.All candidate solutions we examine, feasible or not, becomean innovative database of (biased) samples. Looking be-yond merely finding a solution, database queries aid con-straint reconsideration, active learning, Pareto frontiers,statistical properties, etc. We also present metrics for com-paring populations and tracking their evolutions.

David H. WoodComputer Science DepartmentUniversity of Delawarewood@cis.udel.edu

Steven KimbroughOperations and Information Management DepartmentThe Wharton School of the University of Pennsylvaniakimbrough@wharton.upenn.edu

Balaji PadmanabhanInformation Systems and Decision SciencesUniversity of South Flordiabpadmana@coba.usf.edu ¡bpadmana@coba.usf.edu

CP18

Sensitivity Analysis of Asset Flow OptimizationForecast Algorithm

Asset flow differential equations (AFDE) have been de-veloped and analyzed asymptotically by Caginalp and hiscollaborators since 1989. We study an inverse problem in-volving a semi-unconstrained parameter optimization fora dynamical system of nonlinear AFDE from a challeng-ing financial application on investor population dynamics.We present the sensitivity analysis of AFDE and the cor-responding asset flow optimization forecast algorithm andthe empirical results for a number of closed-end funds trad-ing in US markets.

Ahmet DuranUniversity of Michigan - Ann Arbordurana@umich.edu

Gunduz Caginalp

University of PittsburghDepartment of Mathematicscaginalp@pitt.edu

CP18

Set-Valued Measures of Risk

For optimization problems in Mathematical Finance oneof the objectives is often to minimize the risk of some fi-nancial position. If the investor acts on several markets,under some circumstances risks on different markets cannot be aggregated. Then the use of set-valued measures ofrisk is appropriate. In this paper a complete theory of set-valued risk measures (including primal and dual descrip-tions) along the lines of the real-valued case is developped.The dual description is based on a new duality theory forset-valued maps, introduced recently by one of the authors.

Andreas H. HamelDepartment of Operations Research and FinancialEngineering, Princeton Universityahamel@princeton.edu

Frank Heyde, Markus HohneUniversity of Halle-WittenbergInstitute of Mathematicsfrank,heyde@mathematik.uni-halle.de,markushoehne1981@web.de

CP18

Risk Optimization Using p-Order Conic Con-straints: A Linear Programming Approach

We discuss a class of risk-reward optimization models thatreduce to convex programming problems with p-order conicconstraints. As an illustration, a portfolio optimizationcase study is considered. We develop polyhedral approxi-mation schemes and decomposition algorithms that allowfor efficient implementation of the formulated p-order conicprogramming models as linear programming problems.

Pavlo KrokhmalUniversity of IowaDepartment of Mechanical and Industrial Engineeringpavlo-krokhmal@uiowa.edu

CP18

Optimal Portfolio Execution Strategies and Sensi-tivity to Price Impact Parameters

When liquidating a portfolio of large blocks of risky assets,an institutional investor wants to minimize the cost as wellas the risk of execution. An optimal execution strategyminimizes a weighted combination of the expected valueand the variance of the execution cost, where the weight isgiven by a nonnegative risk aversion parameter. The execu-tion cost is determined from a price impact function. Par-ticularly, a linear price impact model is defined by the tem-porary impact matrix H and the permanent impact matrixΓ, which represent the expected price depression caused bytrading assets at a unit rate. In this paper, we analyze thesensitivity of the optimal execution strategy to estimationerrors in the impact matrices under a linear price impactmodel. We show that, instead of depending on H and Γindividually, the optimal execution strategy is determinedby the combined impact matrix Θ = 1

τ

(H +HT

)− Γ,

where τ is the time length between consecutive trades. Weprove that the minimum expected execution cost strategy

68 OP08 Abstracts

is the naive execution strategy, independent of perturba-tions, when the permanent impact matrix is symmetric andthe combined impact matrix is positive definite. We pro-vide upper bounds on the size of change in the optimal ex-ecution strategy in a general setting. These upper boundsare in terms of the changes in the impact matrices, theeigenvalues of a block tridiagonal matrix defined by thecombined impact matrix, the risk aversion parameter, andthe covariance matrix. These upper bounds indicate that,when the covariance matrix is positive definite, a large riskaversion parameter reduces the sensitivity of the optimalexecution strategy. Moreover, when Γ and its perturbationare symmetric, the optimal execution strategy is asymptot-ically not sensitive to estimation errors when the minimumeigenvalue of either the covariance matrix or the combinedimpact matrix is large. In addition, our computational re-sults confirm that the sensitivity of the optimal executionstrategy to the perturbations decreases, when the perma-nent impact matrix and its perturbation are symmetric.Moreover, the change in the efficient frontier increases asthe risk aversion parameter decreases for asymmetric per-turbations. We consistently observe that imposing shortselling constraints can reduce the sensitivity of the optimalexecution strategy and the efficient frontier.

Somayeh MoazeniSchool of Computer ScienceUniversity of Waterloosmoazeni@uwaterloo.ca

Thomas ColemanDept of Combinatorics and OptimizationUniversity of Waterlootfcoleman@uwaterloo.ca

Yuying LiSchool of Computer ScienceUniversity of Waterlooyuying@uwaterloo.ca

CP18

Quantile-Based Deviation Measures

Quantile-based deviation measures as a class of general de-viation measures, defined by Rockafellar et al., have beenshown to include all lower semicontinuous law-invariant de-viation measures on atomless probability spaces and havebeen established to be consistent with concave ordering.The latter fact has been used to generalize Rao-Blackwelltheorem and to develop an approach for reducing minimiza-tion of quantile-based deviation measures to minimizationof the measures on subsets of undominated random vari-ables with respect to concave ordering. This approachhas been applied for constructing Chebyshev’s and Kol-mogorov’s inequalities with quantile-based deviation mea-sures. As an illustration, Chebyshev’s and Kolmogorov’sinequalities have been derived for mean absolute devia-tion, lower semideviation and conditional value-at-risk de-viation. Also, an example illustrating advantage of Kol-mogorov’s inequality with certain deviation measures inestimating the probability in question has been presented.

Michael Zabarankin, Bogdan Grechuk, Anton MolybohaStevens Institute of Technologymzabaran@stevens.edu, bgrechuk@stevens.edu, amoly-boh@stevens.edu

CP19

An Approach for the Robust Optimization of a Bio-logical Objective in Intensity Modulated RadiationTherapy

Intensity Modulated Radiation Therapy (IMRT) is an ef-fective method for delivering precise radiation doses to tu-mors, while reducing the radiation exposure to surroundingorgans-at-risk and normal tissue. We propose a biolog-ically based convex objective function for the utilizationin treatment plan optimization models. Given clinicallyrepresentable criteria, we show that the resulting convexmodel yields robust treatment plans under possible uncer-tainties in problem data, and illustrate its use on severaltest cases.

Christoffer CromvikDepartment of Mathematical SciencesChalmers University of Technologychristoffer.cromvik@chalmers.se

Karl-Axel JohanssonDepartment of Therapeutic Radiation PhysicsSahlgrenska University Hospitalkarl-axel.johansson@vgregion.se

Caroline OlssonDepartment of Radiation PhysicsSahlgrenska University Hospitalcaroline.olsson@vgregion.se

Michael PatrikssonDepartment of Mathematical SciencesChalmers University of Technologymipat@math.chalmers.se

CP19

A Minimal Surface in Molecular Dynamics Simu-lation of Discoidal High Density Lipoprotein Par-ticles

In a recently concluded work molecular dynamics sim-ulation was used to model the morphology of high densitylipoprotein (HDL) particles composed of an apolipoproteinA-1 ring bounding a palmitoyloleoylphosphatidylcholine(POPC) bi-lipid membrane under incremental removal ofPOPC. The study reports the formation of a minimal sur-face at the interface between two leaflets for one class ofHDL particles. We formulate an energy functional for theexperiment, consisting of the bending energy of a free rib-bon and the surface energy of a membrane and present agradient descent algorithm for minimizing the functional.The minimal surface obtained as the minimizer of the en-ergy functional with the algorithm is compared to that ob-tained from the molecular dynamics simulation.

Mandar S. Kulkarni, Gilbert WeinsteinDepartment of MathematicsUniversity of Alabama at Birminghammandar@uab.edu, weinstei@math.uab.edu

CP19

Sequential Methods for GeneratingMulti-Dimensional Convex Pareto Frontiers

In this presentation, I will discuss a number of new se-quential methods for generating multi-dimensional con-vex Pareto frontiers. Our main motivation for developingthese methods is Intensity Modulated Radiation Therapy

OP08 Abstracts 69

(IMRT). All discussed methods are applicable to higher-dimensional problems. Some of the methods can cover thecomplete Pareto frontier. We also give quality guaranteesfor the approximation quality of the found Pareto frontierto the real Pareto frontier.

Gijs RennenEconometrics and Operations Research, TilburgUniversityg.rennen@uvt.nl

Dick Den HertogTilburg UniversityFaculty of Economics and Business AdministrationD.denHertog@uvt.nl

Edwin R. Van DamTilburg UniversityDept. Econometrics and Operations ResearchEdwin.vanDam@uvt.nl

Aswin HoffmannRadiotherapy Physics Group,Radboud University Nijmegen Medical Centrea.hoffmann@rther.umcn.nl

CP19

A Stable Geometric Buildup Algorithm for the So-lution of the Distance Geometry Problem UsingLeast-Squares Approximation

We propose a geometric buildup algorithm to solve thedistance geometry problem in protein modeling, which canprevent accumulation of rounding errors in calculations,tolerate errors in given distances. In this algorithm, wedetermine each unknown atom by using least-squares ap-proximation instead of exact solution to the system of dis-tance equations. We describe the algorithm, present thetest results to determine a set of protein structures withvarying degrees of availability and accuracy of distances.

Atilla SitIowa State UniversityDepartment of Mathematicsatilla@iastate.edu

Zhijun WuIowa State UniversityDept of Mathzhijun@iastate.edu

Yaxiang YuanLaboratory of Scientific and Engineering ComputingChinese Academy of Scienceyyx@lsec.cc.ac.cn

CP19

Clustered Geometric Buildup

A new method is proposed to solve exact sparse distancegeometry problem in 3D space. To avoid numerical erroraccumulation within incremental geometric buildup algo-rithm, the following approach is used: a structure is par-titioned into overlapping clusters in which the points arecomputed in no more than a predefined number of incre-mental buildup generations. The clusters are aligned usingleast squares method. Results for protein structures with

artificially generated distance data are presented.

Vlad SukhoyIowa State UniversityDepartment of Mathematicssukhoy@iastate.edu

Zhijun WuIowa State UniversityDept of Mathzhijun@iastate.edu

CP20

On the Behrens-Fisher Problem: a Globally Con-vergent Algorithm and a Finite-Sample Study ofthe Wald, Lr and Lm Tests

In this paper we provide the first provably convergent al-gorithm for the multivariate Gaussian Maximum Likeli-hood version of the Behrens-Fisher problem. Moreover,we establish a systematic algebraic relation between theWald, Likelihood Ratio and Lagrangian Multiplier Test(W ≥ LR ≥ LM) in the context of the Behrens-Fisherproblem. The algorithm allows to computationally investi-gate the properties of these tests capturing the role of highdimensionality on the actual size and power of the tests forfinite samples.

Alexandre BelloniDuke UniversityFuqua School of Businessabn5@duke.edu

Gustavo DidierTulane UniversityMathematics Departmentgdidier@tulade.edu

CP20

Construction of Biorthogonal B-Spline TypeWavelet Sequences with Optimal Regularities

In this paper we study the optimal condition for therefinement coefficients of B-spline type scaling functionssuch that the corresponding scaling functions are in L2.Then the B-spline type wavelet sequences possessing thelargest possible regularities and required vanishing mo-ments are characterized, and an optimization algorithmto find such symmetric or antisymmetric B-spline typewavelet sequences is designed.

Tian-Xiao HeIllinois Wesleyan Universitythe@iwu.edu

CP20

Variable Selection via Bridge Regression

Bridge regression searches a family of lp ”norm” penal-ized regressions to chose regression coefficients based ona given model selection criteria. Ridge and lasso regres-sion are special cases of Bridge regression with p = 2 andp = 1,respectively. Lasso is an effective method for vari-able selection because it reduces the number of nonzeroregression coefficients. When 0 < p < 1, even more coef-ficients are forced to zero enhancing the variable selectionproperties of the method. However, when 0 < p < 1 theresulting optimization problem is not only non-convex, it

70 OP08 Abstracts

is non-Lipschitzian. In this talk we propose methods forsolving these non-Lipschitzian optimization problem. Jointwork with James Burke.

Qiuying LinUniversity of Washingtonqiuying@u.washington.edu

James V. BurkeUniversity of WashingtonDepartment of Mathematicsburke@math.washington.edu

CP21

An Object-Oriented Approach to the Implementa-tion of Optimization Algorithms as Abstract Nu-merical Algorithms

Many different optimization algorithms can be expressedin a very abstract form just in terms of basic linear opera-tors, vector operations, scalar products, and linear solves.We have coined the term Abstract Numerical Algorithms(ANAs) to describe such algorithms. This presentation willdescribe the Thyra package and Trilinos object-oriented in-frastructure for the development of such algorithms rang-ing from iterative linear solvers all the way to transientoptimization. These algorithms have been implementedindependent of the computing model but have been runon production applications on some of our largest parallelmachines.

Roscoe A. BartlettSandia National Laboratoriesrabartl@sandia.gov

CP21

Preconditioning for Bound Constrained QuadraticProgramming Problems

Recently proposed MPRGP algorithm for the solutionof strictly convex quadratic programming problems wasproved to enjoy R-linear convergence in bounds on thespectrum. In this talk we consider two methods of pre-conditioning that improved the theoretical rate of conver-gence including nonlinear steps, namely preconditioning bya conjugate projector and edge averaging for the varia-tional inequalities discretized by FETI-DP domain decom-position. Theoretical results are confirmed by numericalexperiments.

Marta Domoradova, Zdenek DostalVSB-TU OstravaDepartement of Applied Mathematicsmarta.domoradova@vsb.cz, zadenek.dostal@vsb.cz

CP21

Optimal Algorithms for Quadratic ProgrammingProblems

We review our results in development of algorithms forbound and/or equality constrained quadratic programmingproblems. Their unique feature is the rate of convergence interms of bounds on the spectrum of the Hessian, indepen-dent of representation of the constraints. When applied tothe class of convex problems with the spectrum in a givenpositive interval and sparse Hessians, the algorithms en-joys optimal complexity. The optimality is demonstrated

on the solution of discretized variational inequalities.

Zdenek DostalVSB-Technical University Ostravazdenek.dostal@vsb.cz

CP21

On Convergence of a Rescaled Lagrangian MethodTo Decompose Structured Convex Programs

In this paper, we propose a new decomposition method forsolving structured optimization problems. The proposedscheme combines the recent decomposition algorithm in-troduced by Hamdi et al. with the nonlinear re-scalingprinciple of Polyak. The resulting algorithm uses the re-cently developed non-quadratic multiplier methods basedon entropy-like proximal methods, to obtain a family ofaugmented lagrangian methods which are twice continu-ously differentiable as opposed to the classical quadraticone. Under mild appropriate assumptions, we show thatthe method generates convergent primal-dual sequences.

Abdelouahed HamdiKuwait Universitywhamdi99@yahoo.fr

CP21

On Convergence Rate of An Algorithm for Mini-mizing Quadratic Functions with Separable ConvexConstraints

A new active set algorithm for minimizing quadratic func-tions with separable convex constraints is proposed by com-bining the conjugate gradient method with gradient pro-jections. It generalizes recently developed algorithms ofquadratic programming constrained by simple bounds. Alinear convergence rate in terms of the Hessian spectralcondition number is proven. Numerical experiments in-cluding frictional 3D contact problems of linear elasticityillustrate the computational performance.

Radek KuceraVSB-TU OstravaDept. of Mathematics and Descriptive Geometryradek.kucera@vsb.cz

CP22

An Algorithmic Framework for a Class of Non-Convex Minlp Problems

Solving non-convex Mixed Integer Nonlinear Program-ming (MINLP) problems with general global-optimizationsolvers is usually very computationally expensive. To someextent this is related to the decomposition of all functionsinto elementary ones. We present an algorithmic frame-work, based on repeated/refined reformulation and approx-imation, targeted at univariate non-convexity, that worksin a geometry that is closer to the original formulation.Computational results are presented.

Claudia D’AmbrosioDEIS - University of Bolognac.dambrosio@unibo.it

Jon Lee, Andreas WaechterIBM T.J. Watson Research Centerjonlee@us.ibm.com, andreasw@us.ibm.com

OP08 Abstracts 71

CP22

A Branch-and-Cut Method for Mixed-0-1 Second-Order Cone Programming

We present a branch-and-cut method for mixed 0-1 second-order cone programming problems. To solve the problemsin the nodes of the branch-and-bound tree, we use a primal-dual interior point method, that converges also for infea-sible starting points. We use different techniques for thegeneration of linear and convex quadratic cuts. The qual-ity of the cuts and their impact on the branch-and-boundprocedure are investigated. Computational results for testproblems and real world applications are given.

Sarah DrewesTechnische Universitat Darmstadt, Department ofMathematicsResearch Group Nonlinear Optimizationdrewes@mathematik.tu-darmstadt.de

Stefan UlbrichTechnische Universitaet Darmstadt, Department ofMathematicsResearch Group Nonlinear Optimizationulbrich @ mathematik.tu-darmstadt.de

CP22

Decomposition Strategies for Mixed Discrete Non-Linear Programming

The proposed paper contributes to the development of thefield of Alternating Optimisation for general Mixed Inte-ger Non-Linear Programming (MINLP), by introducing anew decomposition approach based on the Augmented La-grangian Multipliers method. In the proposed algorithm,the problem has been decomposed to two units, where eachset of variables can be optimised by an efficient solver. Par-ticle Swarm Optimization method is used for optimisingcontinuous variables, while a Genetic Algorithm is appliedfor optimising the discrete variables.

Salam Nema, John Yannis GoulermasUniversity of LiverpoolDepartment of Electrical Engineering and Electronics.salam75@liverpool.ac.uk, j.y.goulermas@liv.ac.uk

CP22

A Method for Optimal Lift Gas Allocation

An optimal allocation procedure and methodology for theGas-Lift optimization problem is presented. In the oil in-dustry, natural gas is often injected into the wellbore toassist fluid production in low producing wells and also tocompensate sub-surface pressure decline. As the lift gas isconstrained and the response to gas injection is non-linear,an optimal allocation is necessary for production maxi-mization. The approach reported is several-fold more effi-cient than traditional approaches for comparable results.

Kashif RashidSchlumberger-Doll Researchkrashid@slb.com

CP22

Computing Safe Dike Heights at Minimal Costs

Safe dike heights are crucial for protecting life in theNetherlands and many other regions of the world. We

discuss issues that arise when modeling the probabilityof floods, the expected damage and measures to preventfloods. Our aim is to minimize the sum of future investingcosts and expected damage over a long period (of about300 years). We present some MINLP optimization mod-els and a dynamic programming model, as well as somecomputational results.

Kees RoosDelft University of Technologyc.roos@tudelft.nl

Dick Hertog, DenUniversity of TilburgThe Netherlandsd.denhertog@uvt.nl

CP23

A Trust-region Filter-SQP Method for Mathemat-ical Programs with Linear Complementarity Con-straints

A trust-region filter-SQP method for mathematical pro-grams with linear complementarity constraints (MPLCC)is proposed. We solve a sequence of the relaxed problemswith some parameter driven to zero and use the filter tech-nique presented by Fletcher and Leyffer [Math. Program.,Ser. A, 91: 239-269 (2002)] to promote the global conver-gence. Under mild assumptions, it is proved that every ac-cumulation point of the generated iterates is either a strongstationary point or an infeasible stationary point of theMPLCC. Our test problems are originated from the QPEC-gen generator and include the programs with quadratic andnon-quadratic objective functions. Some numerical resultsare reported, which show that the presented method is veryeffective.

Chun-Lin Hao, Xin-Wei LiuDepartment of Applied Mathematics,Hebei University of Technologychunlin.hao@gmail.com, mathlxw@hebut.edu.cn

CP23

LPCC Approach to Nonconvex Quadratic Pro-grams

This talk presents a novel approach to general nonconvexquadratic programs by reformulating them as linear pro-grams with linear complementarity constraints (LPCC).The cornerstone of the approach is a parameter-free mini-max integer program formulation of the LPCC, which leadsto a finite Benders-type algorithm that involves solvingsatisfiability subproblems. Computational results are re-ported on randomly generated problems with two types ofconstraints: box constraints and general linear constraints,including problems with unbounded feasible regions.

Jing HuRensselaer Polytechnic Institutejasmine.hu@gmail.com

Jong-Shi PangUniversity of Illinois at Urbana-Champaignjspang@uiuc.edu

John E. MitchellRensselaer Polytechnic Institute110, 8th Street, Troy, NY, 12180mitchj@rpi.edu

72 OP08 Abstracts

CP23

Optimal Control of Elliptic ComplementarityProblems in Function Space: C-Stationarity anda Multigrid-Based Solution Scheme

We consider mathematical programs with complementar-ity constraints (MPCC) in function space. Typical modelproblems are related to optimal control of variational in-equalities (VIs) or parameter identification in VIs. Basedon a smoothed penalization technique C-stationarity isachieved. The proposed algorithm is numerically real-ized using a semismooth Newton-based full approximationscheme in a multigrid framework. The results are com-pared to those of an alternative relaxation-method and areport on numerical tests is given.

Ian KopackaUniversity of Graz,START-Project Interfaces and Free Boundariesian.kopacka@uni-graz.at

Michael HintermuellerUniversity of Sussex, United KingdomDepartment of Mathematicsmichael.hintermueller@uni-graz.at

CP23

An �1 Elastic Method for Mathematical Programswith Equilibrium Constraints and Degenerate Pro-grams

We extend an �1-elastic framework to the context ofMPECs. The resulting smooth equality-constrained sub-problems satisfy the MFCQ and are solved using a pre-conditioned interior-point method. Under reasonable as-sumptions, we establish global convergence to a stronglystationary point provided the penalty parameter remainsbounded. We present an implementation of the elasticframework for MPECs and preliminary numerical results.We emphasize how the approach also applies to other typesof mathematical programs failing to satisfy the MFCQ.

Dominique OrbanDept. Mathematics and Industrial EngineeringEcole Polytechnique de MontrealDominique.Orban@polymtl.ca

Zoumana CoulibalyGERAD and Ecole Polytechnique de Montrealzoumana.coulibaly@gerad.ca

CP23

Structural Topology Optimization Problems For-mulated As Mathematical Programs with Equilib-rium Constraints

We consider the technological very important problem offinding minimal weight designs for structural topology op-timization problems with local stress constraints. Theproblems are formulated as Mathematical Programs withVanishing Constraints (MPVC) and as Mathematical Pro-grams with Complementarity Constraints. Some of thetheoretical advantages and disadvantages are discussed.We also report several numerical experiments that sub-stantiate the conclusion that MPVCs give a more compu-tational efficient representation for this class of structuraltopology optimization problems.

Marie-Louise H. Rasmussen

Department of MathematicsTechnical University of Denmarkm.l.h.rasmussen@mat.dtu.dk

Wolfgang AchtzigerUniversity of DortmundGermanywolfgang.achtziger@uni-dortmund.de

Mathias StolpeDepartment of MathematicsTechnical University of DenmarkM.Stolpe@mat.dtu.dk

CP24

Randomized Algorithms for Nonlinear Optimiza-tion overBipartite Matchings and Matroid Intersections

We consider a broad generalization of the standard lin-ear combinatorial problem which includes a d-dimensionalweight vector for each element and a functional on d-dimensional space. We compute the objective value apply-ing the functional on the feasible solution weight vector, i.e.the sum of the weight vectors in the corresponding solution.While the problem is generally intractable, we provide ran-domized algorithms, polynomial for fixed d, for optimizingarbitrary objectives over bipartite matchings and matroidintersections.

Yael BersteinTechnion – Israel Institute of Technologyyaelber@technion.ac.il

Shmuel OnnTechnion - Israel Institute of Technologyonn@ie.technion.ac.il

CP24

The Graph Embedding and Its Application to QAP

We introduce a technique for 0-1 integer programmingthat exploits hypergraph partitioning constraints to pro-duce tight semidefinite program relaxations. We appliedthe method to quadratic assignment problems and testedon 22 QAP benchmark problems. The method producedSDP bounds within 5% of optimal on average and gen-erated optimal solutions in 10 cases (5 provably optimal).This is the first polynomial time algorithm to achieve prov-ably optimal solutions on any of the benchmark problems.

Changhui ChoiUniversity of Colorado, DenverChanghui.Choi@cudenver.edu

Stephen BillupsUniversity of Colorado at Denverstephen.billups@cudenver.edu

CP24

Path-Based Lp Model of the Set Partitioning Prob-lem

In this talk, we will present a new, graph-based model-ing approach and a polynomial-sized linear programming(LP) formulation of the Set Partitioning Problem (SPP).The approach will be illustrated with a numerical example.

OP08 Abstracts 73

Computational testing and results will be discussed.

Moustapha DiabyUniversity of Connecticutmoustapha.diaby@business.uconn.edu

CP24

The 2-Dimensional Probabilistic Bin Packing Prob-lem

In the probabilistic two-dimensional Bin Packing problem(2D-PBPP), one is asked to pack a random number of rect-angular items, without overlap and any rotation, into theminimum number of identical square bins. In this paper weconsider the two procedures used for solving probabilisticcombinatorial optimization problems : The re-optimizationprocedure and the a priori one and we focused in theirasymptotic behavior through simulations. According tocomputational results we show that under precise condi-tions, the best a priori procedure which is a simple methodgenerates results near those given by the re-optimizationstrategy which is impossible to carried out.

Leila HorchaniLaboratoire Cristal , Pole GRIFT, Tunisialeila.horchani@gmail.com

Monia BellalounaENSI Campus Universitaire de la Manouba Tunisiamonia.bellalouna@ensi.rnu.tn

CP25

Optimizing Stability For Polynomial Families

Given a family of polynomials {p}x whose coefficients de-pend smoothly on the parameter x ∈ Rk, we seek x∗ tominimize the maximum real part of the roots of the corre-sponding polynomial px∗ . This problem is non-smooth,non-convex, and has important applications in stabilitytheory. I consider an approach based on the Routh-Hurwitz conditions, and give some properties of the epi-graph of the feasible set.

Jonathan A. CrossUniversity of Washingtonjacross@math.washington.edu

CP25

Variational Analysis of Functions of the Roots ofPolynomials

In 2001 Burke and Overton showed that the abscissa map-ping on polynomials is subdifferentially regular on themonic polynomials of degree n in the linear space of polyno-mials of degree n. This result is significant for its impacton problems involving optimal stability. In this talk wediscuss extensions of this result to a more general class offunctions of the roots of polynomials which includes boththe abscissa and radius mappings for polynomials.

Julia Eaton, James V. BurkeUniversity of WashingtonDepartment of Mathematicsjreaton@u.washington.edu, burke@math.washington.edu

CP25

Advances on the Bessis-Moussa-Villani Trace Con-jecture

A long-standing conjecture asserts that the polynomial

p(t) = Tr[(A+ tB)m]

has nonnegative coefficients whenever m is a positive inte-ger and A and B are any two n × n positive semidefiniteHermitian matrices. The conjecture arises from a questionraised by Bessis, Moussa, and Villani (1975) in connectionwith a problem in theoretical physics. Their conjecture, asshown recently by Lieb and Seiringer, is equivalent to thetrace positivity statement above. In this paper, we derivea fundamental set of equations satisfied by A and B thatminimize or maximize a coefficient of p(t). Applied to theBessis-Moussa-Villani (BMV) conjecture, these equationsprovide several reductions. In particular, we prove that itis enough to show that (1) it is true for infinitely many m,(2) a nonzero (matrix) coefficient of (A+ tB)m always hasat least one positive eigenvalue, or (3) the result holds forsingular positive semidefinite matrices. Moreover, we provethat if the conjecture is false for some m, then it is false forall larger m. Finally, we outline a general program to settlethe BMV conjecture that has had some recent success.

Christopher J. HillarTexas A&M UniversityDept. Mathematicschillar@math.tamu.edu

CP25

Disjunctive Cuts for Non-Convex Mixed IntegerQuadratically Constrained Programs

This paper addresses the problem of generating strongconvex relaxations of Mixed Integer Quadratically Con-strained Quadratic Programs (MIQQP). MIQQP is avery difficult class of problems because it combines twokinds of non-convexities: integer variables and non-convexquadratic constraints. To produce strong relaxations ofMIQQP we use techniques from disjunctive programmingand lift-and-project. In particular we propose new meth-ods for generating valid inequalities by using the equationY = xxT . We use the concave constraint Y - xxT ¡ 0to derive disjunctions of two types. The first ones are di-rectly derived from the eigenvectors of the matrix Y - xxTwith positive eigenvalues, the second type of disjunctionsare obtained by combining several eigenvectors in order tominimize the width of the disjunction. We also use the con-vex SDP constraint Y - xxT ¿ 0 to derive convex quadraticcuts and combine both approaches in a cutting plane algo-rithm. We present series of computational experiments onbox-QPs of moderate size.

Anureet SaxenaCarnegie Mellon Universityanureet@cmu.edu

Pierre BonamiAix-Marseille Universite - CNRSpierre.bonami@gmail.com

Jon LeeIBM T.J. Watson Research Centerjonlee@us.ibm.com

CP26

Scalar Versus Vector Optimization Problems In-

74 OP08 Abstracts

volving Risk Functions

Many risk functions were recently introduced (coherent riskmeasures, generalized deviations, etc.) and many financialproblems were revisited. The use of new risk functionsis well justified by the rapid evolution of financial mar-kets and products, but final results often depend on theconcrete risk function one draws on. We consider vectoroptimization problems involving several risk functions andstudy if the involved objectives may be reduced to a singleone capturing every required property.

Alejandro Balbas, Beatriz BalbasUniversity Carlos III of Madridbalbas@mathstat.concordia.ca, beatriz.balbas@uc3m.es

CP26

Conic Scalarization in Finite-Dimensional VectorOptimization

Scalarization approaches to solving vector optimizationproblems for Pareto optimal points are reviewed and modi-fied for the generation of solutions that are non-dominatedwith respect to convex cones. The corresponding scalar-valued optimization problems are formulated, classified aslinear or nonlinear cone programs, and solved using recenttechniques from conic optimization. Based on preliminarycomputational results, the relevance and implications ofusing general cones for trade-off or preference modeling inmulti-objective programming and decision-making are ad-dressed.

Alexander EngauUniversity of WaterlooDepartment of Management Sciencesaengau@uwaterloo.ca

CP26

Interior Point Warmstarts Applied to StochasticProgramming

We describe a method of generating a crash-start pointfor interior point methods in the context of stochastic pro-gramming. We construct a small-scale version of the prob-lem corresponding to a reduced event tree and use its so-lution to generate an advanced starting point for the com-plete problem. The reduced tree is constructed by sce-nario aggregation in order to capture information from thescenario space while keeping the dimension of the corre-sponding (reduced) deterministic equivalent small. Inte-rior point methods struggle in general to take advantageof such information. We derive conditions on the reducedtree that guarantee a successful interior point warm-startfor the complete problem. We present numerical results ona range of test problems which shows remarkable advan-tages of this approach.

Andreas GrotheySchool of MathematicsUniversity of EdinburghA.Grothey@ed.ac.uk

Marco ColomboUniversity of Edinburghm.colombo@ed.ac.uk

Jacek GondzioThe University of Edinburgh, United KingdomJ.Gondzio@ed.ac.uk

CP26

Multi-Objective Design of a Combinatorial Struc-ture

A problem of configuring a population of trucks is ad-dressed. The resulting model is a multi-objective optimiza-tion problem. We formulate a (single objective) optimiza-tion problem to find the best representation of the Paretooptimal set under the constraint that the configurationsare built up by common parts. The solution process is alsoextended to the case when the underlying objective func-tions are expensive. Results when applying the model to asmall industrial example are reported.

Peter LindrothDepartment of Mathematical SciencesChalmers University of Technology / Volvo 3Ppeter.lindroth@math.chalmers.se

Michael PatrikssonDepartment of Mathematical SciencesChalmers University of Technologymipat@math.chalmers.se

Ann-Brith StrombergFraunhofer-Chalmers Centre for Industrial Mathematicsannbrith@fcc.chalmers.se

CP27

A Grid-Based Adaptive Simulated AnnealingMethod for Global Optimization

A grid-based hybrid method is built that is essentiallybased on simulated annealing technique. However, this al-gorithm processes and stores information in several lists asthe optimization method tabu does. This technique contin-uously adjusts the step sizes for different parameters suit-ably and builds an appropriate annealing schedule in anadaptive manner. The method is implemented on differenttest functions; comparison centered on accuracy and effi-ciency is performed with a variant of simulated annealingmethod.

Urmi Ghosh-DastidarNew York City College of Technology (CUNY)ughosh-dastidar@citytech.cuny.edu

CP27

Optimization of Parallel Codes on Cluster of Com-puters

Genetic Algorithms are known to be robust and suitableto parallel processing, becoming an attractive approach inthe field of numerical optimization. In the research areaof aerodynamic optimization, using Computational FluidDynamics, the computational efficiency is a major concern.Assuming that a parallel algorithm consists of consecutivestages, a Genetic Algorithm is proposed to find the opti-mum number of processors and data distribution methodto be used for each stage of the parallel algorithm.

Marcel IlieCarleton UniversityDepartment of Mechanical and Aerospace Engineeringmilie@connect.carleton.ca

CP27

A New Interval Partitioningapproach for Con-

OP08 Abstracts 75

strained Optimization

This paper is concerned with solving the continuous Con-strained Optimization Problems (COP) with general con-straints and objective function. We propose an efficientinterval partitioning method (IP) where a new subdivisiondirection method and an adaptive tree search approach aredefined. In the adaptive tree search, nodes are explored us-ing a restricted hybrid depth-first and best-first branchingstrategy, whereas the new parallel subdivision direction se-lection rule targets directly the uncertainty degrees of con-straints (with respect to feasibility) and the uncertaintydegree of the objective function (with respect to optimal-ity). Reducing these uncertainties as such results in theearly detection of infeasible and sub-optimal boxes that arediscarded reliably. The effectiveness of the proposed IP isillustrated on COP benchmarks and compared with com-mercial global and local solvers. Key Words: Constrainedglobal optimization, interval partitioning with local search,adaptive search tree management, subdivision direction se-lection rules

Chandra Sekhar PedamalluNew England Biolabs Incpedamallu@neb.com

Linet OzdamarYeditepe University, Department of Systems EngineeringKayisdagi, Istanbul, Turkey.linetozdamar@lycos.com

Janos PosfaiNew England Biolabs, Inc.240 County Road, Ipswich, MA 01938, USA.posfai@neb.com

CP27

A Multistart Approach for Continuous Global Op-timization Using a Pseudo-Convexity Criterion

We develop a novel multistart approach for continuousglobal optimization of expensive functions. In this method,we cluster previously evaluated points such that the datapoints corresponding to each cluster belong to the graph ofa pseudo-convex function. Then, we start a local optimiza-tion solver from each cluster. After obtaining new localoptimization trajectories, we evaluate additional points inunexplored regions, update the clusters, and then, iteratethe procedure. We shall present some numerical results.

Rommel G. RegisSaint Joseph’s Universityrregis@sju.edu

Shane HendersonCornell UniversitySchool of Operations Research and Industrial Engineeringsgh9@cornell.edu

Christine ShoemakerCornell Universitycas12@cornell.edu

CP27

Low Discrepancy Point Sets Used in Interval Algo-rithms for Global Optimization

Low discrepancy point sets and low discrepancy sequencesare widely used in simulation and estimation algorithms in

science, engineering, finance, industry, and statistical in-ference. Their application to global optimization is mostlylimited to the so-called quasirandom search methods. Thistalk discusses various usages of them in the framework ofinterval algorithms for global optimization. Preliminarynumerical test results will show what usages are effectiveand what are not.

Min SunUniv. of AlabamaMath Deptmsun@gp.as.ua.edu

CP28

Sensitivity Analysis for Decentralized Process Con-trol Problems

In this presentation we focus on decentralization of large-scale process control problems. Starting with the Inter-action Prediction Principle, we focus on sensitivity issuesrelated to the IPP algorithm and stress that the sensitivityof the overall problem is strongly related to the sub-units.The main result is that different decompositions schemescan lead, under appropriate assumptions, to different sen-sitivity results for the overall problem.

Anes DallagiUniversity of Albertadallagi@ualberta.ca

Fraser ForbesUniversity of AlbertaDept of Chemical & Materials Engineeringfraser.forbes@ualberta.ca

CP28

Structured Fixed-Order H-infinity Controller De-sign

Built upon methods for non-smooth optimization, Hifooattempts to compute optimal, reduced-order controllers forlinear systems. We present extensions to Hifoo allowingthe user to input plants with non-trivial feedthrough aswell as specify structure on the controller. Finally, Hi-foo is applied to try to solve problems in simultaneousstabilization, a known undecidable problem. Numericalexperiments are provided for realistic systems, includingthe control of an industrial web-winding system and struc-tured, static-output-feedback control of an F-16.

Marc MillstoneCourant Institute of Mathematical SciencesNew York Universitymillstone@cims.nyu.edu

Michael L. OvertonNew York UniversityCourant Instit. of Math. Sci.overton@cs.nyu.edu

CP28

On Logarithmic Smoothing and Strongly StableStationary Points

We consider the problem (P) of minimizing a function overa feasible set M . By using a logarithmic barrier function,we construct a family Mγ of interior point approximationsof M where Mγ is described by a single smooth inequal-

76 OP08 Abstracts

ity constraint. Under the assumption that all stationarypoints of (P) are strongly stable we show that there is aone-to-one correspondence between the stationary pointsof (P) and those of (Pγ) where the latter problem is ob-tained from (P) by substituting M by Mγ . Furthermore,corresponding stationary points of (P) and (Pγ) have thesame stationary index. The lecture is based on a joint pa-per with Hubertus Th. Jongen.

Jan-J. RuckmannThe University of Birmingham, United Kingdomruckmanj@maths.bham.ac.uk

CP28

Minimization of Costs in Supply Networks withTransportation and Decision-Making Delays

Due to delays in product transportation and decision-making, supply network dynamics is governed by infi-nite dimensional differential equations, stability of whichis non-trivial to analyze. A unique map revealing stabil-ity/instability behavior of the supply network is obtainedin the parameter space of the delays, first. Next, an op-timization scheme is proposed to choose stabilizing trans-portation delays that minimize a cost function related totransportation costs and excessive oscillations in invento-ries. A case study is provided.

Rifat Sipahi, Ilker DeliceDepartment of Mechanical and Industrial EngineeringNortheastern Universityrifat@coe.neu.edu, delicei@coe.neu.edu

Tucker MarionSchool of Technological EntrepreneurshipNortheastern Universityt.marion@neu.edu

CP28

Optimal Grid Synthesis in Control Problems ofPrescribed Duration.

Optimal control problems are considered under assump-tions that dynamics are nonlinear and running terminal-integral costs are minimized along trajectories on giventime intervals. Data are assumed to be Lipschitz con-tinuous relative phase variables. A numerical method issuggested to construct optimal grid synthesis. It is basedon a backward procedure of integrating Hamiltonian differ-ential inclusions, and on results of the theory of minimax/ viscosity solutions of the Bellman equation. Results ofsimulations are exposed.

Nina N. SubbotinaInstitute of Mathematics and MechanicsUral Branch of the Russian Academy of Sciencessubb@uran.ru

Timofey B. TokmantsevInstitute of Mathematics and Mechanics,Ural Branch of the Russian Academy of Sciences, Russiatokmantsev@imm.uran.ru

CP29

Design of Electron Devices Using 3D SimulationCodes and Computer Optimization

Computer optimization can explore a larger parameter

space than practical with manual design, particularly for3D geometries. This allows rapid, economical developmentof higher performance devices. The proliferation of para-metric solid modeling programs allows optimization of bothgeometry and operating parameters. This presentation willdescribe computer optimization in the 3D trajectory codeBeam Optics Analysis (BOA). In particular, using (BOA)software, we design and model a sheet-beam electron gun,which has the advantage of lower operating voltage, im-proved efficiency, and greater bandwidth. The physical pa-rameters of the electron gun are then optimized for severaldifferent physical goals using parametric modeling softwareand various sampling based optimization algorithms. Re-sults are presented along with a detailed treatment of theoptimization methodology.

Adam AttarianNC State Universityarattari@unity.ncsu.edu

Hien T. TranNorth Carolina State UnivDepartment of Mathematicstran@math.ncsu.edu

Lawrence Ives, Thuc BuiCalabazas Creek Research, Inc.rli@calcreek.com, bui@calcreek.com

CP29

From a Fast Optimization Scheme for the Estima-tion of Velocity Fields to Image Data Assimilation

We consider the assimilation of satellite images, withinthe framework of data assimilation in geophysical systems.Based on the constant brightness assumption, we define anonlinear functional measuring the difference between twoconsecutive images, the first one being transported to thesecond one by the unknown velocity. By considering amultiscale approach and a Gauss-Newton minimization al-gorithm, we can estimate the entire velocity fields at a highframe rate and then assimilate these pseudo-observations.

Didier Auroux, Jerome FehrenbachUniversity of Toulouseauroux@mip.ups-tlse.fr, fehren@mip.ups-tlse.fr

CP29

Convex Iteration for Constraining Cardinality andRank with Application to Compressive Sampling

We present a numerical technique, called convex iteration,originally conceived for constraining rank in semidefiniteprogramming. The technique possesses an analog for con-straining cardinality. Recent results from compressed sens-ing (a.k.a, compressive sampling) theory establish cardi-nality as a lower bound on number of measurements re-quired to obtain perfect reconstruction. We present exam-ples, from signal processing and particularly Magnetic Res-onance Imaging (MRI), achieving that lower bound whileretaining perfect reconstruction. We demonstrate robust-ness of the algorithm in presence of noise.

Jon Dattorroconvexoptimization.comdattorro@stanford.edu

OP08 Abstracts 77

CP29

Nonnegative Matrix Factorization and Underap-proximation

Nonnegative Matrix Factorization (NMF) is a compres-sion technique which allows interpretation of nonnegativedata, with applications in image processing, text mining,etc. We study an extension called Nonnegative Factoriza-tion (NF) consisting in finding the best approximation ofa not-necessarily nonnegative matrix by a product of twolow-rank nonnegative matrices and use it within a new un-derapproximation technique (NMU) particularly efficientat achieving sparse solutions for NMF. We also show NP-hardness of both (NF) and (NMU).

Nicolas B. GillisUniversite catholique de LouvainCenter for Operation Research and Econometricsnicolas.gillis@uclouvain.be

Franois GlineurUniversite catholique de LouvainCenter for Operations Research and Econometricsfrancois.glineur@uclouvain.be

CP29

Optimization Methods for Improving Video Fieldof View

The field of view of modern digital video cameras can besignificantly increased by optically superimposing differentregions of a scene and then computationally disambiguat-ing the superimposed frames. The aim of this process is togenerate a high resolution, wide field of view video with-out a large and potentially expensive detector array. Inthis talk, we present computational methods for solvingthe disambiguation problem associated with such a system.Building upon existing optimization methods for solvingthe �2 − �1 minimization problem associated with staticcompressed sensing, we develop a fast approach designedto exploit the dynamics of the video setting. Simulationand experimental results demonstrate the effectiveness ofthis approach over non-dynamic approaches.

Roummel F. MarciaDepartment of Electrical and Computer EngineeringDuke Universityroummel@ee.duke.edu

Rebecca WillettElectrical and Computer EngineeringDuke Universitywillett@duke.edu

CP30

Resource-Constrained Scheduling in ComputerGames

This paper studies a resource-constrained project schedul-ing problem. Consider a set of tasks each of which is as-sociated with three parameters: the amount of requiredresources, the amount of returned resources and the pro-cessing time. Given an initial resource level, we want to de-termine a feasible mission sequence such that we can meetthe target resource level in the earliest time. In this paper,we design and analyze several approximation algorithms.

Bertrand LinDepartment of Information and Finance Management

National Chiao Tung University (TAIWAN)bmtlin@mail.nctu.edu.tw

Kueitang FangInstitute of Information ManagementNational Chiao Tung University (TAIWAN)jacky0831@gmail.com

CP30

Design of Fixed-Order Robust Controllers via Non-smooth Optimization

HIFOO (H-infinity fixed-order optimization) is a MATLABpackage for fixed-order controller design using nonsmooth,nonconvex optimization. We discuss the practical appli-cation of HIFOO to solve real-world problems from theengineering literature. We also introduce a new versionof HIFOO that is designed to find controllers that, in ad-dition to achieving good performance and robustness, arealso strongly stable. Benchmarks on real-world problemsare presented.

Suat GumussoyThe MathWorks Inc.suat.gumussoy@mathworks.com

Marc MillstoneCourant Institute of Mathematical SciencesNew York Universitymillstone@cims.nyu.edu

Michael L. OvertonNew York UniversityCourant Instit. of Math. Sci.overton@cs.nyu.edu

CP30

Hybrid Optimization Techniques for Hydrody-namic Stability Control

We propose a numerical scheme for the solution of prob-lems of hydrodynamic stability control. In that contextwe consider shape optimization problems in flow controlwhere the stability issues are represented by eigenvalueconstraints. We investigate approaches based on a combi-nation of derivative-free and gradient-based methods withfocus on an adequate treatment of the eigenvalue function.Moreover, techniques relying on high-performance comput-ing are used to solve the resulting large highly nonlinearsystems.

Vincent Heuveline, Frank StraussUniversity of Karlsruhevincent.heuveline@rz.uni-karlsruhe.de,frank.strauss@rz.uni-karlsruhe.de

CP30

Convex Conic Formulation of Upper Bound Ele-ment Techniques in Metal Forging

The upper bound element technique (UBET) is an alterna-tive to finite element methods for engineering problems inapplied plasticity. UBET requires solving sequences of non-smooth optimization problems that reflect the dynamic ge-ometry of the workpiece and the need to evaluate compet-ing manufacturing designs. We show that, in the contextof metal forging, UBET problems can be reformulated interms of sparse convex conic optimization. We also present

78 OP08 Abstracts

some preliminary computational results.

Stephen E. WrightMiami UniversityDept of Math & Statisticswrightse@muohio.edu

MS1

Nonsmooth Algorithms for Nonlinear SemidefiniteProgramming

Applications to automatic control have been among thedriving forces to develop methods for nonlinear semidefi-nite programming (NL-SDP). For instance, the Kalman-Yakubovic-Popov Lemma leads to programs subject to bi-linear matrix inequality (BMI) constraints. These BMIsare hard to solve due to a strong disparity between theunknown controller gains and the Lyapunov variables. Forsizeable systems, the best results are to date obtained bynonsmooth optimization methodes [1]. For H infinity syn-thesis a new line was proposed in [2], where the use ofLyapunov variables can be avoided. In this presentationwe develop these ideas further and address several inter-esting applications, like parametric robustness [3] or mixed(multi-objective) control [4]. [1] P. Apkarian, D. Noll, O.Prot. A trust region spectral bundle method for noncon-vex eigenvalue optimization. 2007. [2] P. Apkarian, D.Noll. Nonsmooth H infinity control. IEEE Trans. Au-tom. Control. 51, no. 1, 2006, 71-86. [3] P. Apkarian,D. Noll, O. Prot. Nonsmooth methods for control designwith IQCs. 2007. [4] P. Apkarian, D. Noll, A. Rondepierre.Mixed H2/H infinity control via nonsmooth optimization.2007.

Dominikus NollUniversite Paul SabatierInstitut de Mathematiquesnoll@mip.ups-tlse.fr

Olivier ProtLaboratoire MIPUniversite Paul Sabatieroprot@mip.ups-tlse.fr

Pierre ApkarianONERA-CERTapkarian@cert.fr

MS1

A New First Order Method for Non-LinearSemidefinite Programming

A new method for the efficient solution of nonlinear op-timization problems with matrix variables is introduced.The method is based on the sequential convex program-ming concept. The main idea is to approximate nonlinearfunctions defined in matrix variables by sequences of blockseparable, convex functions. The resulting subproblemsare convex semidefinite programs with a favorable struc-ture, which can be efficiently solved by the code PENNON.Convergence results as well as numerical experiments arepresented. Finally it is shown how the method can be gen-eralized for the solution of standard nonlinear semidefiniteprograms.

Michael StinglInstitut fur Angewandte MathematikUniversitat Erlangen-Nurnberg, Germanystingl@am.uni-erlangen.de

MS1

A Derivative Free Method for Nonlinear SDPs

At the moment, most available algorithms for SDPs aim atthe efficient solution of (high dimensional) linear, maybeeven nonlinear, problems. Most methods therefore relyon first or even second-order information. In contrast tothis, we will focus on a completely derivative-free methodfor nonlinear SDPs. We will highlight both theoreticaland practical aspects of the algorithm, which actually isthe derivative-free version of the penalty-barrier-multipliermethod used for example in pennon.

Ralf WernerHypo Real Estate Holding AGwerner ralf@gmx.net

MS1

Primal-Dual Interior Point Methods for NonlinearSDP Problem

In this talk, a class of primal-dual interior point meth-ods for nonlinear SDP problems will be presented. It willbe shown that globally convergent primal-dual algorithmswhich are similar to methods for usual nonconvex NLPproblems can be developed for nonconvex NLSDP prob-lems. Various possibilities for search strategy includingline search and trust region methods, for merit function se-lection including primal funtion and primal-dual function,along with our numerical experiment will be presented.

Hiroshi YamashitaMathematical Systems Inc.hy@msi.co.jp

MS2

A Class of Inexact Null Space Iterations in PDE-Constrained Optimization

Based on linearly convergent iterative solvers for the stateand the adjoint equation, respectively, a preconditioned it-erative scheme for the KKT-system of class of discretizedPDE-constrained minimization problems is proposed. Ev-ery step of the outer loop may be interpreted as a SQP-type step. The inner loop consists essentially of two parts:approximate feasibility restoration and a step towards op-timality. The globalization is based on a �1 line search. Aconvergence analysis of the method is provided and numer-ical results are presented.

Michael HintermuellerUniversity of Sussex, United KingdomDepartment of Mathematicsmichael.hintermueller@uni-graz.at

Volker SchulzUniversity of TrierDepartment of MathematicsVolker.Schulz@uni-trier.de

MS2

An Adjoint Approach to Shape Optimization inComputational Fluid Dynamics

We consider shape optimization problems governed by thestationary incompressible Navier-Stokes equations. In con-trast to fully discrete methods the shape derivatives arecomputed analytically by using a continuous adjoint-based

OP08 Abstracts 79

approach. For the stationary problem we use pseudo-timemarching in connection with preconditioning and suitabletime stepping schemes that can be applied in parallel forthe state and adjoint equation. Numerical results will bepresented.

Florian LindemannTechnical University of MunichGermanylindemann@ma.tum.de

Christian BrandenburgTU DarmstadtGermanybrandenburg@mathematik.tu-darmstadt.de

Michael UlbrichTechnical University of MunichChair of Mathematical Optimizationmulbrich@ma.tum.de

Stefan UlbrichTechnische Universitaet DarmstadtFachbereich Mathematikulbrich@mathematik.tu-darmstadt.de

MS2

Numerical results with a Multilevel Trust-RegionMethod in Infinity Norm

We present a multilevel trust-region method in infinitynorm for both unconstrained and bound constrained opti-mization. The main feature of the new method is to allowthe exploitation, in a trust-region framework, of the factthat many large-scale optimization problems have a hier-archy of different descriptions, possibly involving differentnumber of variables. The important features and parame-ters of the algorithm are described. Extensive umerical re-sults are presented on a set of problem arising in PDE basedoptimization. The general behaviour of the algorithm isanalysed first as a function of its parameters. Comparisonwith other optimization algorithms is also provided.

Melodie MouffeCERFACSFrancemelodie.mouffe@cerfacs.fr

Serge GrattonCERFACSToulouse, Franceserge.gratton@cerfacs.fr

Philippe L. TointThe University of NamurDepartment of Mathematicsphilippe.toint@fundp.ac.be

Dimitri TomanosFUNDPNamur, Belgiumdtom@math.fundp.ac.be

MS2

A Posteriori Error Estimators Based on WeightedKKT-Residuals for Adaptive Control Constrained

Optimization with PDEs

We introduce a concept for reliable a posteriori error esti-mators for a class of control constrained optimization prob-lems with PDEs (including elliptic or parabolic problems).We show that an appropriate weighted residual (in func-tion space) of the KKT-conditions, which is motivated byinterior point methods, yields a reliable error estimator forapproximate solutions of the optimality system. For finiteelement discretizations this residual can be estimated ele-mentwise by using standard error estimators, which resultsin a reliable error estimator for adaptive mesh refinement.Numerical results are presented.

Stefan UlbrichTechnische Universitaet DarmstadtFachbereich Mathematikulbrich@mathematik.tu-darmstadt.de

MS3

Error Estimates in the Approximation of OptimalControl Problems Governed by Quasilinear EllipticEquations

In this talk we consider an optimal control problem gov-erned by the quasi-linear elliptic equation

−div[a(x, y(x))∇y(x)] + f(x, y(x)) = u(x) in Ω, (1)

y(x) = 0 on Γ (2)

where a(x, y) ≥ α > 0 and f is monotone non-decreasingwith respect to the second variable. The goal is to carryout the numerical analysis of the control problem providingsome error estimates of the approximations. Though thestate equation is well posed, the uniqueness of a solutionof the discrete state equation is an open problem. In theanalysis the following steps are performed:

• The discrete state equations are locally well posed andwe obtain error estimates for the approximations.

• We prove that strict local minima of the control prob-lem can be approximated by local minima of the dis-crete problems.

• By assuming that a local minimum satisfies the suffi-cient second order optimality condition, we get errorestimates for the discrete approximations.

Eduardo CasasUniversidad de CantabriaETSI Ind y de Telecommeduardo.casas@unican.es

Fredi TroeltzschTech Univ of BerlinDepartment of Mathematicstroeltz@math.tu-berlin.de

MS3

A Moreau-Yosida Based Regularization Scheme forPointwise State Constraints in PDE-ConstrainedOptimization

The generalized Moreau-Yosida regularization of the char-acteristic function of several classes of pointwise state con-straints in optimal control of PDEs is considered. Its flex-ibility allows to treat different constraint types (such asdistributed or boundary constraints) within one unifyingframework. Under a mild assumption we derive existenceof Lagrange multipliers as well as the convergence of the

80 OP08 Abstracts

regularization scheme. A function space based solutionmethod is introduced and its convergence is analysed. Thetalk ends by a report on numerical tests.

Michael HintermuellerUniversity of Sussex, United KingdomDepartment of Mathematicsmichael.hintermueller@uni-graz.at

MS3

Neuman and Dirichlet Boundary Control - OptimalConvergence Rates and Numerical Implementation

We discuss tailored discretization concepts for elliptic Neu-mann and Dirichlet boundary control problems and proveoptimal error bounds on the control variables. We presentnumerical examples which confirm our analytical findings.

Michael HinzeUniversitat HamburgDepartment Mathematikhinze@math.uni-hamburg.de

MS3

The Goal Oriented Dual Weighted Approach forControl and State Constrained Elliptic OptimalControl Problems

We consider primal-dual weighted goal oriented a poste-riori error estimates for pointwise control and state con-strained optimal control problems associated with secondorder elliptic partial differential equations. The estimatorsare derived within the framework of the goal oriented dualweighted approach. They consist of primal-dual residu-als, primal-dual weighted error terms representing the mis-match in the complementarity system due to discretization,and data oscillations. In case of sufficiently regular active(or coincidence) sets and problem data, a further decom-position of the multiplier into a regular L2-part on the ac-tive set and a singular part concentrated on the boundarybetween active and inactive set allows a further character-ization of the mismatch error. Numerical results are givento illustrate the performance of the error estimators.

Ronald HoppeUniversity of HoustonUniversity of Augsburgrohop@math.uh.edu

Michael HintermuellerUniversity of Sussex, United KingdomDepartment of Mathematicsmichael.hintermueller@uni-graz.at

MS4

An Outer-Approximation Approach to MaximumEntropy Sampling with Quadratic Constraints

This work presents an outer-approximation algorithm formaximum entropy sampling with quadratic constraints. Anew mixed-integer semidefinite program formulation thatemploys binary variables to indicate the selection of a sam-pling point, and exploits the linear equivalent form of a bi-linear term involving binary variables to ensure convexity.An outer-approximation algorithm that obtains the opti-mal solution by solving a sequence of mixed-integer linearprograms is developed. Numerical experiments verify the

computational effectiveness of the proposed method.

Han-Lim ChoiMassachusetts Institute of TechnologyAerospace Controls Laboratoryhanlimc@mit.edu

Jonathan P. HowAerospace Controls LaboratoryMassachusetts Institute of Technologyjhow@mit.edu

Paul I. BartonMassachusetts Institute of TechnologyDepartment of Chemical Engineeringpib@mit.edu

MS4

Pump-Based Heuristics for Mixed-Integer Nonlin-ear Programming

Abhishek KumarLehigh UniversityDepartment of Industrial and Systems Engineeringkua3@Lehigh.EDU

MS4

A Lifted Linear Programming Branch-and-BoundAlgorithm for Mixed Integer Conic Quadratic Pro-grams

We develop a linear programming based branch-and-boundalgorithm for mixed integer conic quadratic programs,which is based on a higher dimensional or lifted polyhe-dral relaxation of conic quadratic constraints introducedby Ben-Tal and Nemirovski. We present results of compu-tational experiments on a series of portfolio optimizationproblems and show that the algorithm significantly outper-forms commercial and open source solvers based on bothlinear and nonlinear relaxations.

Juan Pablo Vielma, Shabbir Ahmed, George NemhauserH. Milton Stewart School of Industrial & SystemsEngineeringGeorgia Institute of Technologyjvielma@isye.gatech.edu, sahmed@isye.gatech.edu,george.nemhauser@isye.gatech.edu

MS5

Polynomial Optimization Techniques for SecondOrder PDEs and Optimal Control Problems

To solve a partial differential equation (PDE) numeri-cally, we formulate it as a polynomial optimization problem(POP) by discretizing it via a finite difference approxima-tion. The resulting POP satisfies a structured sparsity,which we exploit by applying the sparse SDP relaxation ofWaki et al. to obtain an approximate solution of the PDE.Moreover, we take into account the particular structure ofPOP’s feasible set, determined by equality constraints, toreduce the size of the sparse SDP relaxation.

Martin MevissenTokyo Institute of TechnologyDepartment of Mathematical and Computing Sciencesmevissen.m.aa@m.titech.ac.jp

OP08 Abstracts 81

Masakazu KojimaTokyo Institute of Technologykojima@is.titech.ac.jp

Nobuki TakayamaKobe Universitytakayama@math.kobe-u.ac.jp

MS5

Semidefinite (SDP) Representation of Convex Sets

A set S ⊂ Rn is called SDP representable if S equals theprojection of a set in Rn+N describable by some LMI.Clearly, the necessary conditions are S must be convexand semialgebraic. This talk discusses sufficient conditionsand necessary conditions for SDP representability. We willprove: (1) Suppose S = {x : g1(x) ≥ 0, ..., gm(x) ≥ 0}is a compact convex set defined by polynomials. ThenS is SDP representable if each gi(x) is sos-concave, i.e.,−∇2gi(x) = W (x)TW (x) for some possibly nonsquare ma-trix polynomial W (x). (2) For a general compact convexsemialgebraic set S, we prove the sufficient condition: theboundary of S is positively curved, and the necessary con-dition: the boundary of S has nonnegative curvature atsmooth points and on nondegenerate corners. A sufficientcondition bypassing the gaps is when some defining poly-nomials are sos-concave.

Jiawang NieUniversity of California, San Diegonjw@math.ucsd.edu

J. William HeltonMath. DeptUC San Diegohelton@math.ucsd.edu

MS5

Optimization with Polynomials

Optimization problems involving multivariate polynomialsare ubiquitous in many areas of engineering and appliedmathematics. Although these problems can sometimes(but not always) be approached using the traditional ideasof nonlinear optimization, in recent years there has beenmuch interest in new techniques, that exploit their intrin-sic algebraic features, to provide global solutions and/ormore efficient algorithms. In this talk we survey the ba-sic features of these algebraic approaches, involving sum ofsquares (SOS) and semidefinite programming, emphasiz-ing the geometric aspects and a few selected applicationsin dynamical systems and game theory.

Pablo A. ParriloMassachusetts Institute of Technologyparrilo@MIT.EDU

MS5

Perfect Point Configurations

We study a problem of Lovasz as to when a real point con-figuration has the property that all linear polynomials thatare non-negative over the points are also sums of squaresof linear polynomials modulo a radical zero-dimensionalideal whose variety has exactly these given points as thereal points in it. This leads to a generalization of Lovasz’ztheta body for a graph to all polytopes which is a semidef-

inite relaxation of the polytope.

Rekha Thomas, Joao GouveiaUniversity of Washingtonthomas@math.washington.edu,jgouveia@math.washington.edu

Pablo A. ParriloMassachusetts Institute of Technologyparrilo@MIT.EDU

MS6

A Variant of the Augmented Lagrangian Methodwith Faster Dual Convergence

In this talk we discuss a variant of the augmented La-grangian method in which a different update rule is usedto generate the sequence of dual Lagrange multipliers.Arithmetic-complexity results are derived for two stoppingrules in the context of a special but broad class of convexprograms. Specializations of these results are also derivedin the context of the cone programming problem.

Guanghui LanSchool of ISyEGeorgia Techglan@isye.gatech.edu

MS6

A Primal-Dual First-Order Method for LinearCone Programming

We first reformulate a linear cone programming into aprimal-dual smooth convex minimization problem over amanifold. Then we discuss Nesterov’s smooth methodfor solving them, and the associated iteration-complexitybound is discussed. The proposed method is finally appliedto solve some large-scale linear cone programming prob-lems arising from compressed sensing. The computationalresults show that this method substantially outpeforms in-terior point methods, and is very promising to solve thisclass of large-scale problems.

Zhaosong LuDept. of MathematicsSimon Fraserzhaosong@cs.sfu.ca

MS6

Arithmetic-Complexity of Augmented LagrangianAlgorithms.

In this talk, we discuss arithmetic-complexity results for aclassical optimization algorithm, namely: the augumentedLagrangian method, in the context of a special but broadclass of convex programs. In particular, we present spe-cialization of these complexity results in the context of theconic programming problem.

Renato C. MonteiroGeorgia Institute of TechnologySchool of ISyEmonteiro@isye.gatech.edu

MS6

An ACCPM Algorithm for Support Vector Ma-

82 OP08 Abstracts

chine Classification with Indefinite Kernels.

In this paper, we propose a method for support vector ma-chine classification using indefinite kernels. Instead of di-rectly minimizing or stabilizing a nonconvex loss function,our method simultaneously finds the support vectors and aproxy kernel matrix used in computing the loss. This canbe interpreted as a robust classification problem where theindefinite kernel matrix is treated as a noisy observationof the true positive semidefinite kernel. Our formulationkeeps the problem convex and relatively large problems canbe solved efficiently using the analytic center cutting planemethod. We compare the performance of our techniquewith other methods on several data sets.

Ronny LussPrinceton Universityrluss@princeton.edu

Alexandre d’AspremontORFE, Princeton Universityaspremon@Princeton.EDU

MS7

Title TBD

Charles Audetcole Polytechnique de Montreal - GERADCharles.Audet@gerad.ca

MS7

Title TBD

Luis N. VicenteUniversity of Coimbralnv@mat.uc.pt

MS8

Robust Optimization to the Rescue of Chance Con-straints

We study conic optimization problems affected by stochas-tic uncertainty under partial information on the underly-ing probability distribution functions. In the Chance Con-straints (CC) approach feasibility is required to hold withat least a given probability. Such problems are notoriouslydifficult. We show that the Robust Optimization method-ology can offer safe and tractable approximations to theseCC problems.

Aharon BentalSchool of Industrial Engineering and ManagementTechnion, Israelabental@ie.technion.ac.il

MS8

Robust Discrete Optimization

Abstract not available at time of publication.

Dimitris BertsimasMassachusetts Insitute of Technologydbertsim@mit.edu

MS8

Less is More: Robustness and Sparsity in Multi-variate Statistics

We describe applications of robust optimization in the con-text of machine learning, with a focus on classificationand regression, principal component analysis and fittingof graphical models. In these tasks, sparsity of the solu-tion is often desired as it provides ways to interpret theresult. In a classification problem for example, the spar-sity pattern of the classifier vector allows to identify thefeatures that are most discriminative. We will explore theconnections between sparsity and robustness and illustratethese connections in the context of genomic data, as wellas social data, such as voting records and online news.

El G. LaurentEECS, U.C. Berkeleyelghaoui@eecs.berkeley.edu

MS8

Robust Optimization in Multi-Period Problems

We discuss computational tractability of Affinely Ad-justable Robust Counterpart of an uncertain Linear Pro-gramming problem, with emphasis on a generic applica-tion, specifically, on computationally efficient design ofaffine control rules for an uncertainty-affected linear dy-namical system ensuring that the state-control trajectoryon a given finite horizon satisfies in a robust fashion a sys-tem of linear inequalities.

Arkadi NemirovskiSchool of Industrial and Systems EngineeringGeorgia Technemirovs@isye.gatech.edu

MS9

Active-Set Approaches to Basis Pursuit Denoising

Many imaging and compressed sensing applications seeksparse solutions to large under-determined least-squaresproblems. The basis pursuit (BP) approach minimizes the1-norm of the solution, and the BP denoising (BPDN) ap-proach balances it against the least-squares fit. The dualsof the BP and BPDN problems are conventional linear andquadratic programs. We explore the effectiveness of active-set approaches for solving large-scale BP and BPDN prob-lems.

Michael P. FriedlanderDept of Computer ScienceUniversity of British Columbiampf@cs.ubc.cca

Michael SaundersSystems Optimization Laboratory (SOL)Dept of Management Sci and Eng, Stanfordsaunders@stanford.edu

MS9

Iterative Signal Recovery From Incomplete and In-accurate Measurements

Compressive Sampling (CoSa) offers a new paradigm foracquiring signals that are compressible with respect to anorthobasis. The major algorithmic challenge in CoSa isto approximate a compressible signal from noisy samples.

OP08 Abstracts 83

Until recently, all provably correct reconstruction tech-niques have relied on large-scale optimization, which tendsto be computationally burdensome. This talk describes anew iterative, greedy recovery algorithm, called CoSaMPthat delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorousbounds on computational cost and storage. It is likely tobe extremely efficient for practical problems because it re-quires only matrix–vector multiplies with the sampling ma-trix. For many cases of interest, the running time is justO(N ∗ logp(N)), where N is the length of the signal and pis a small integer.

Joel TroppApplied and Computational MathematicsCaltechjtropp@acm.caltech.edu

Deanna NeedellMathematics, UC Davisdneedell@math.ucdavis.edu

Roman VershyninMathematicsUniversity of California at Davisvershynin@math.ucdavis.edu

MS9

Sparse Reconstruction via Separable Approxima-tion

Finding sparse approximate solutions to large underdeter-mined linear systems of equations is a common problem insignal/image processing and statistics. One standard ap-proach is to minimize the sum of a quadratic error termand a sparsity-inducing (usually �1) regularization term.We propose iterative methods in which each step is ob-tained from an optimization subproblem involving a sep-arable quadratic term plus the original sparsity-inducingterm. Our approach handles group-separable regularizersin addition to the standard �1 regularizer.

Stephen J. WrightUniversity of WisconsinDept. of Computer Sciencesswright@cs.wisc.edu

Robert NowakUniversity of WisconsinElectrical and Computer Engineeringnowak@ece.wisc.edu

Mario T. FigueiredoInstituto Superior TecnicoInstituto de Telecomunicacoesmario.a.t.figueiredo@gmail.com

MS9

First-Order Methods for Constrained and Uncon-strained �1-Minimization Problems

We propose simple and efficient methods for solving theproblems minu μ‖u‖1+‖Au−f‖2/2 and minu{‖u‖1 : Au =f}, respectively, which are used in compressed sensing.Our method for the unconstrained problem is based onoperator splitting and continuation. We show that thismethod obtains the support and signs of the optimal solu-tion in a finite number steps, and achieves a q-linear global

convergence speed. Our method for the constrained prob-lem is based on Bregman iterative regularization and yeildsan exact solution after solving only a very small number ofinstances of the unconstrained problem above for f = fk

given. We show analytically that this iterative approachis equivalent to the method of multipliers. Both methodsare especially useful for many compressed sensing appli-cations where matrix-vector operations involving A and A′

can be computed by fast transforms. We were able to solvehuge instances of compressed sensing problems quickly ona standard PC.

Wotao YinRice Universitywotao.yin@rice.edu

Elaine HaleCAAMRice Universityehale@rice.edu

Yin ZhangRice UniversityDept of Comp and Applied Mathyzhang@caam.rice.edu

Stanley J. OsherUniversity of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

Donald GoldfarbColumbia Universitygoldfarb@columbia.edu

Jerome DarbonMathematicsUCLAjerome@math.ucla.edu

MS10

Optimizing the Probe Placement for Radio-Frequency Ablation

The focus of this talk will be on the RF ablation of livertumors with mono- or bipolar systems. To achieve a com-plete destruction of the lesion, one has to consider a num-ber of various effects as for example the cooling influence ofblood vessels and the patient individual tissue properties.In this talk different approaches towards an optimization ofthe RF probe placement (as e.g. an optimization with ananalytic approximation of the electric potential, a multi-scale optimization, and a stochastic optimization takingthe uncertainty in the tissue parameters into account) willbe discussed. Moreover, applications of the optimizationto artificial test scenarios as well as to a real RF ablationwill be presented.

Inga Altrogge

Center of Complex Systems and Visualization (CeVis)University of Bremen, Germanyaltrogge@cevis.uni-bremen.de

MS10

Identification of Tissue Properties for Thermal Ab-lation

We focus on the identification of thermal and electrical

84 OP08 Abstracts

conductivities for thermal ablation, e.g. radio-frequencyablation. From measurement data of the temperature dis-tribution the parameters are reconstructed by formulatingthe inverse problem as an optimal control problem. Thus,we solve a minimization problem with the heat equationand the potential equation as constraints, and where thosetwo equations are coupled through source terms of the heatequation. We use a finite element method to solve the con-straining PDE system. Various examples demonstrate theperformance of our approach.

Carmeliza L. NavascaRochester Institute of Technologycnavasca@gmail.com

Hanne TieslerCenter of Complex Systems and Visualization (CeVis)University of Bremenhanne.tiesler@cevis.uni-bremen.de

MS10

Identification of Perfusion and Antenna Profiles inRegional Hyperthermia

In the cancer therapy regional hyperthermia, the mostprominent modeling errors stem from the highly individ-ual perfusion arising in the bio-heat transfer equation. Thetalks presents identification of the perfusion based on MRthermography data, aiming at both, quality assessmentand online reoptimization. A second area affected by sev-eral sources of model errors is the computation of specificabsorption rates. A possibility to improve the SAR modelagain using MR thermography will be discussed.

Martin WeiserZuse Institute (ZIB)Berlin, Germanyweiser@zib.de

MS11

A Fast Method for Finding the Global Solutionof the Regularized Structured Total Least SquaresProblem for Image Deblurring

Given a linear system Ax ≈ b where both the structuredmatrix A and the vector b are subject to noise, the struc-tured total least squares(STLS) problem seeks to find acorrection matrix and a correction righthand side vector ofminimal norm which makes the linear system feasible whilemaintaining the structure of A. To avoid ill-posedness, aregularization term is added to the objective function; thisleads to the so-called regularized STLS (RSTLS) problem.In general this problem is nonconvex and hence difficultto solve. However, we show that problem can be globallyand efficiently solved for structures arising from image de-blurring applications under reflexive or periodic boundaryconditions. The devised method is based on decomposingthe problem into single variable problems and then trans-forming them into 1D unimodal real-valued minimizationproblems which can be globally solved. Based on unique-ness and attainment properties of the RSTLS solution weshow that a constrained version of the problem possess astrong duality result and can thus be solved via a sequenceof RSTLS problems.

Amir BeckFaculty of Industrial Engineering and ManagementTECHNION - Israel Institute of technologybecka@ie.technion.ac.il

Aharon Ben-TalTechnion - Israel Institue of TechnologyIsraelabental@ie.technion.ac.il

Christian KanzowUniversity of Wuerzburgkanzow@mathematik.uni-wuerzburg.de

MS11

Augmented Primal-Dual Method for Linear ConicPrograms

We propose a new iterative approach for solving linear pro-grams over convex cones. Assuming that Slater’s condi-tion is satisfied, the conic problem is transformed to theminimization of a certain convex differentiable function.The evaluation of the function and its derivative is cheapif the projection of a given point onto the cone can becomputed cheaply, and if the projection of a given pointonto the affine subspace defining the primal problem canbe computed cheaply. For the special case of a semidef-inite program, a certain regularization of this function isanalyzed. Numerical examples illustrate the potential ofthe approach.

Florian JarreMathematisches InstitutUniversitaet Duesseldorf, Germanyjarre@opt.uni-duesseldorf.de

Franz RendlUniversitaet Klagenfurtrendl@uni-klu.ac.at

Thomas DaviUniversitaet Duesseldorf, GermanyMathematisches Institutdavi@opt.uni-duesseldorf.de

MS11

Robust Limit Analysis of Steel Structures

We study the problem of limit analysis of elastic structures,i.e., problem of finding the maximal multiplier of a givenload, such that the new load can still be supported by thestructure. This is measured by the von Mises failure cri-terion. The problem can be formulated as an SOCP. Wewill assume that the loads are not exact, rather perturbedby small perturbation loads lying in an ellipsoid. The ro-bust counterpart to our SOCP is then a linear SDP. Wewill compare solutions of this SDP with solutions of ap-proximate robust counterparts due to Bertsimas and Simand to Goldfarg and Iyengar. We will show that, for thisparticular problem, the exact robust counterpart is far su-perior to the approximate ones. We will further show thatthe so-called shake-down analysis due to G. Maier is a spe-cial approximate robust counterpart of the standard limitanalysis problem.

Michal KocvaraSchool of MathematicsUniversity of Birminghamkocvara@penopt.com

Christos BisbosDepartment of Civil EngineeringAristotle University of Thessaloniki

OP08 Abstracts 85

cbisbos@civil.auth.gr

MS11

Matrix Convex Functions and Optimization

In this talk, we discuss various differentiation rules for gen-eral smooth matrix-valued functions, and for the class ofmatrix convex (or concave) functions first introduced byLowner and Kraus in the 1930s. For a matrix monotonefunction, we present formulas for its derivatives of any or-der in an integral form. Moreover, for a general smoothprimary matrix function, we derive a formula for all of itsderivatives by means of the divided differences of the orig-inal function. As applications, we use these differentiationrules and the matrix concave function logX to study a newnotion of weighted centers for Semidefinite Programming(SDP). We show that, with this definition, some knownproperties of weighted centers for linear programming canbe extended to SDP. We also show how the derivative for-mulas can be used in the implementation of barrier meth-ods for optimization problems involving nonlinear but con-vex matrix functions. This talk is based on a joint paperwith Jan Brinkhuis and Tom Luo.

Shuzhong ZhangThe Chinese University of Hong KongShatin, Hong Kongzhang@se.cuhk.edu.hk

MS12

A Multilevel Algorithm for Inverse Problems withElliptic PDE Constraints

We propose a multilevel algorithm for the solutionTikhonov-regularized first-kind Fredholm equations. Weconsider a source identification problem in which the for-ward problem is an elliptic partial differential equation.Our method assumes the availability of an approximateHessian operator for which, first, the spectral decomposi-tion is known, and second, there exists a fast algorithm thatcan perform the spectral transform. Based on this decom-position we propose a Conjugate Gradients solver which weprecondition with a multilevel subspace projection scheme.We demonstrate the effectiveness of our method with the2D-Neumann Poisson problem with variable coefficientsand partial observations.

George BirosUniversity of Pennsylvaniabiros@seas.upenn.edu

Gunay DoganSchool of Engineering and Applied ScienceUniversity of Pennsylvaniagdogan@seas.upenn.edu

MS12

Shape Optimization Governed by the Linear Elas-ticity Equations

Using sheet metal forming a wide variety of different pro-files can be manufactured. We apply shape optimizationto help find the optimal design for a given application.We present an efficient multilevel SQP-method for thenon-convex geometry optimization of sheet metal profiles,which is also suited for other design problems. We usedetailed PDE-based models, e.g., 3D linear elasticity forstiffness optimization, which is the focus of this talk, or

the heat equation. Numerical results are presented.

Wolfgang Hess, Stefan UlbrichTechnische Universitaet DarmstadtFachbereich Mathematikwhess@mathematik.tu-darmstadt.de,ulbrich@mathematik.tu-darmstadt.de

MS12

Numerical Methods for Experimental Design of Ill-Posed Problems

In this talk we present a method for the design of experi-ments in the context of parameter identification problems.We develop a new methodology based on empirical riskminimization, that enable us to use modern PDE optimiza-tion methods for the design of such experiments.

Eldad HaberEmory UniversityDept of Math and CShaber@mathcs.emory.edu

Lior HoreshEmory Universitylhoresh@emory.edu

MS12

Computing Hessian Approximations for PartiallySeparable Unconstrained Optimization

In Newton-like methods, computing Hessian, or some denseapproximation, represents a serious obstacle to solve large-scale unconstrained optimization problems because of thestill limited computation resources and memory capacities.Fortunately, these problems often have a partially separa-ble structure. We present and compare several ways toaproximate Hessian taking advantage of this property with-out requiring more than function and gradient evaluations.Some numerical experiences inside a recursive multileveltrust-region algorithm are also presented. A better inte-gration in this framework is currently under investigationby trying to use information from approximate invariantsubspaces and multisecant equations.

Vincent MalmedyUniversity of NamurBelgiumvincent.malmedy@fundp.ac.be

MS13

Interface Evolution: A Control Problem with H1-and H−1-Norms in the Cost Functional

Interface evolution with mass conservation can be mod-elled by the Cahn-Hilliard equation, which is a variationalinequality of fourth order. Discretizing in time the corre-sponding gradient flow equation results into a control prob-lem with control constraints and with a cost functional in-cluding the H1-semi-norm as well as the norm of the dualspace H−1. Hence, we face problems similar to controlproblems with state constraints. First we present shortlythe existence results for the control. As main focus of thistalk we discuss the application of the primal-dual activeset method, analyse its convergence behaviour and presentnumerical results. One further aspect is the efficient so-lution of the resulting linear systems having saddle pointstructure. This freedom of choosing a linear algebra solver

86 OP08 Abstracts

is one advantages of using the primal-dual method insteadof other simulation approaches. A further advantage is theenourmos reduction of the dimension due to small inactivesets. A short outlook on interface evolution without massconservation with the Allen-Cahn variational inequality isgiven at the end.

Luise BlankNWF I - MathematikUniversitat Regensburgluise.blank@mathematik.uni-regensburg.de

MS13

Structure Exploiting A-Priori and A-PosterioriDiscretization Concepts for Elliptic Optimal Con-trol Problems in the Presence of Gradient Con-straints

We consider optimal control problems subject to an elliptic(possibly nonlinear) partial differential equation with con-straints on the gradient of the state. We introduce a tay-lored appropriate discretization concept. The state equa-tion is discretized with the help of lowest order RaviartThomas mixed finite elements to cope with possible dis-continuities for the control and the adjoint state. In orderto solve the discretized problems efficiently structure ex-ploiting numerical solution algorithms are discussed. Fur-thermore optimal error estimates for the numerical finiteelement solution are presented. In the context of goal-oriented adaptivity the DWR concept proposed by Beckerand Rannacher for PDE-constrained optimization is ex-tended to our framework. With the help of an error repre-sentation in the objective local error indicators are defined.Their performance properties are investigated by means ofnumerical examples.

Andreas GuntherUniversity of Hamburg, Germanyandreas.guenther@math.uni-hamburg.de

Klaus DeckelnickOtto-von-Guericke-University Magdeburgklaus.deckelnick@mathematik.uni-magdeburg.de

Michael HinzeUniversitat HamburgDepartment Mathematikhinze@math.uni-hamburg.de

MS13

Balancing Regularization and Discretization Er-ror in the Virtual Control Concept for State-Constrained Optimal Control Problems withBoundary Control

We consider a linear quadratic optimal control problemwith pointwise state constraints and cont rol constraints,where the control acts at the boundary. It is well knownthat problems with pointwise state constr aints inhibit alot of difficulties since the Lagrange multipliers are in gen-eral only Borel measures. Therefore, d ifferent regulariza-tion concepts are developed in the last years. However, adirect extension of the Lavrentiev reg ularization conceptis not possible since the control is not defined in the do-main where the state constraints are given. We will usethe concept of a virtual distributed control in the domainΩ. Thus the Lavrentiev regularization is applicable. Theeffect of regularization is influenced by different parameterfunctions depending on a regulari zation parameter ε > 0.

Furthermore, the problem is discretized by finite elements.We derive an error es timate of the optimal solution ofthe original problem to the corresponding discretized andregularized one. Since the regularization error and the dis-cretization error appears simultaneously, we have to bal-ance the regularization parameter and the mesh size in anappropriate manner.

Klaus Krumbiegel, Arnd RoeschUniversity Duisburg-Essenklaus.krumbiegel@uni-due.de, arnd.roesch@uni-due.de

Christian MeyerWIAS, Berlinmeyer@wias-berlin.de

MS13

Feedback Stabilization of the Navier-Stokes Equa-tions by a Boundary Control of Finite Dimension

We are interested in the stabilization of the Navier-Stokesequations in a neighbourhood of an unstable stationnarysolution. When the Reynolds number becomes largeenough the discretization of the equations requires a highnumber of degree of freedom. In that case the numerical so-lution of the Riccati equation needed to define a feedbackcontrol cannot be calculated. In this talk we shall showthat a control of finite dimension is sufficient to stabilize(locally) the full nonlinear equation. This kind of resulthas been already obtained in the case of a distributed con-trol, but in our knowledge is new in the case of a boundarycontrol.

Laetitia SerinUniversite Paul Sabatier, Toulouseserin@mip.ups-tlse.fr

MS14

Acyclic and Star Coloiring Algorithms for HessianComputation

The following four-step procedure makes the computationof a sparse Hessian H using automatic differentiation effi-cient: determine the sparsity pattern of H; using an appro-priate graph coloring, obtain a seed matrix S; compute thecompressed Hessian B ≡ HS; recover the values of the en-tries of H from B. We discuss novel algorithms developedwithin CSCAPES for each of these steps, with emphasison the coloring step. We also sketch a framework for par-allelizing greedy coloring algorithms.

Assefaw GebremedhinOld Dominion UniversityCompter Science Departmentassefaw@cs.odu.edu

MS14

Pattern Graphs for Sparse Matrices

Abstract not available at time of publication.

Shahadat HossainDepartment of Mathematics and Computer ScienceUniversity of Lethbridgeshahadat.hossain@uleth.ca

OP08 Abstracts 87

MS14

Coloring Hierachical Derivative Matrices

Discretizing PDEs on a regular grid induces a hierarchyof two types of sparsity patterns on a Jacobian matrix,one due to the stencil being used and one due to the de-pendence among individual degrees of freedom within thatstencil. Goldfarb and Toint demonstrated how to exploitthe sparsity structure induced by the stencil, but exploit-ing the unstructured sparsity within the stencil must relyupon more general techniques. We present a two stagecoloring strategy: Goldfarb-Toint coloring followed by op-timal intra-stencil coloring. We demonstrate that optimalcoloring at both stages is suboptimal in general. Nonethe-less, savings of 50% or more over Goldfarb-Toint alone arepossible.

Paul D. HovlandArgonne National LaboratoryMCS Division, 221/C236hovland@mcs.anl.gov

MS14

Sparsity Detection for Jacobians and Hessians inADOL-C

Abstract not available at time of publication.

Andre WaltherInstitute of Scientific ComputingTechnical University Dresdenandrea.walther@tu-dresden.de

MS15

Overview of the Minisymposium, and Recent Re-sults on the Application of Semidefinite Program-ming to Characterize Satisfiability

This presentation will first provide a brief overview of theminisymposium. Second, a new semidefinite programmingrelaxation for the satisfiability problem will be presented.This relaxation is an extension of previous relaxations aris-ing from the paradigm of partial semidefinite liftings for0/1 optimization problems. It is shown that the relaxationis exact for Tseitin instances with no restrictions on theirstructure, meaning that the instance is unsatisfiable if andonly if the corresponding semidefinite relaxation is infeasi-ble.

Miguel F. AnjosDepartment of Management SciencesUniversity of Waterlooanjos@stanfordalumni.org

MS15

Solving Minimum k-Partition Problems UsingSemidefinite Programming

The minimum k-partition (MkP) problem is the problemof partitioning the set of vertices of a graph into k disjointsubsets so as to minimize the total weight of the edgesjoining vertices in the same partition. Our main contribu-tion is the design and implementation of a branch-and-cutalgorithm based on semidefinite programming (SBC) forthe MkP problem. The two key ingredients for this algo-rithm are: the combination of semidefinite programmingwith polyhedral results; and a novel iterative clusteringheuristic (ICH) that finds feasible solutions for the MkPproblem. The SBC algorithm computes globally optimal

solutions for dense graphs with up to 60 vertices, for gridgraphs with up to 100 vertices, and for different values ofk, providing the best exact approach to date for k ≥ 3.

Bissan GhaddarDepartment of Management SciencesUniversity of Waterloob3ghadda@engmail.uwaterloo.ca

Miguel F. AnjosDepartment of Management SciencesUniversity of Waterlooanjos@stanfordalumni.org

Frauke LiersInstitut fur InformatikUniversitat zu Kolnliers@informatik.uni-koeln.de

MS15

Solving Quadratic 0-1 and Max-Cut Problems bySemidefinite Programming

In this talk we present a method for finding exact solutionsof the Max-Cut problem (MC), an NP-hard combinatorialoptimization problem. This method is based on a relax-ation of MC using Semidefinite Programming (SDP) com-bined with a polyhedral relaxation by incorporating theso-called triangle inequalities. We use a branch and boundframework, applying this relaxation as upper bound. Thecomputation of this upper bound is done by a dynamicversion of the bundle method. This algorithm has beenintroduced as Biq Mac - a solver for Binary Quadratic andMax-Cut problems. Besides explaining in detail the algo-rithm, we also present many numerical results, collected asBiq Mac Library. Furthermore, we review other solutionapproaches and compare the numerical results with ourmethod. The experiments show, that our method nearlyalways outperforms all other approaches. In particular,where Linear Programming based methods fail (i.e. densegraphs) our method performs very well. Exact solutionsare obtained in reasonable time for any instance of size upto n=100 vertices, no matter what density. Various testproblems that have been considered in the literature foryears, were solved by Biq Mac for the first time.

Franz RendlUniversitat KlagenfurtInstitut fur Mathematikfranz.rendl@uni-klu.ac.at

Giovanni RinaldiIstituto di Analisi dei Sistemi ed Informatica del CNRrinaldi@iasi.cnr.it

Angelika WiegeleAlpen-Adria-Universitaet Klagenfurtangelika.wiegele@uni-klu.ac.at

MS15

Local Branching with Semidefinite Relaxations

We investigate the application of semidefinite relaxationsto the Local Branching scheme that was recently intro-duced for integer programming problems. Our motivationis two-fold: First, we aim to improve the Local Branchingframework through higher-quality starting solutions andstronger relaxations. Second, we aim to develop search

88 OP08 Abstracts

heuristics to efficiently apply semidefinite relaxations tocombinatorial problems. We demonstrate our findings ex-perimentally on different problem domains, including sta-ble set and max-2sat problems.

Willem-Jan van HoeveTepper School of Business, Carnegievanhoeve@andrew.cmu.edu

Andrea LodiDEIS, University of Bolognaandrea.lodi@unibo.it

MS16

T -Algebras and Linear Optimization Over Sym-metric Cones

The first target-following algorithm was given by ShinjiMizuno in 1992 for linear complementarity problems, us-ing the notion of delta sequences. The delta sequence is asequence of targets that lead the primal-dual solutions to-wards optimality. This target-following paradigm was suc-cessfully generalized to semidefinite programming by thespeaker in a recent work. In this talk, the target-followingframework is further generalized to symmetric cone pro-gramming via T -algebra.

Chek Beng ChuaNanyang Technological Universitycbchua@math.uwaterloo.ca

MS16

Invariance Properties of Extremal Ellipsoids of aConvex Body

Let K be a convex body in a finite dimensional Euclideanspace. The minimum volume ellipsoid circumscribing Kand the maximum volume ellipsoid inscribed in K are twoof the best known ellipsoids associated with K. The el-lipsoids inherit any symmetry properties of the underlyingbody K. In this talk, we concentrate on the symmetry prop-erties of these ellipsoids (and some others). Among others,we are interested in (a) investigation of how the symmetriesof a body K influences some of its geometric characteris-tics, (b) explicit computation of the ellipsoids for classes ofconvex bodies K which have special symmetry properties,(c) classification of convex bodies with special symmetryproperties, (d) using all these results to develop efficientalgorithm for optimization problems.

Osman GulerUniversity of Maryland, Baltimore Countyguler@math.umbc.edu

MS17

Optimization of Model and Computational Param-eters in Expensive Engineering Simulations

This talk describes our efforts to reduce computationaltime in optimization problems that require expensive engi-neering simulations. It is motivated by a class of problemsin which each function evaluation requires both a Navier-Stokes hydrodynamic simulation process and an image reg-istration process to recover from a reference image of a fluidcertain unknown model parameter values. In the suggestedapproach, computational parameters, such as the grid sizeof the underlying simulation are treated as variables sothat the fidelity of the simulation can be relaxed during

the optimization process, thus saving computational time.Surrogate functions are formed both on function values andon computational times and used in a way that pushes theoptimization process to less expensive regions of the do-main. Numerical results show that this approach has greatpotential for handling these types of problems.

Mark AbramsonAFITmark.abramson@afit.edu

Thomas AsakiLos Alamos National Laboratoryasaki@lanl.gov

David BetheaAir Force Institute of Technologydavid.bethea@afit.edu

John E. Dennis, JrRice Universitydennis@caam.rice.edu

Matthew SottileUniversity of Oregonmatt@cs.uoregon.edu

MS17

Some New Results in Derivative Free Optimization

I am hoping they are new so I don’t know what they areyet!

Andrew ConnIBM Thomas J. Watson Research Centerarconn@us.ibm.edu

MS17

Towards Multi-Objective Optimization Using Di-rect Search

This talk presents a direct search algorithm for multi-objective optimization that finds a Pareto set solution forproblems that are either unconstrained or subject to linearconstraints. A Pareto solution set gives a number of solu-tion alternatives that aim to represent the relative trade-off between several objectives. We also show that the ap-proach is well suited for parallelization. We give numericalresults for this method on a small set of problems.

Rakesh KumarThe MathWorks, Inc.Rakesh.Kumar@mathworks.com

MS17

Issues of Polynomial Regression and Noisy Func-tions in Derivative Free Optimization

Derivative free optimization methods are known to be rea-sonably successful in dealing with noisy black box func-tions. However, most of the theory of derivative free opti-mization so far was developed in the absence of noise. Wewill discuss theoretical issues that arise from consideringnoisy function. In particular, we will discuss how the con-ditions on sampling sets change when one uses polynomialregression rather than interpolation.

Katya Scheinberg

OP08 Abstracts 89

T.J. Watson Research Center, IBM, P.O.Box 218Yorktown Heights, NY 10598katyas@watson.ibm.com

MS18

Rational Learning in Networks

We study a model of rational learning for self-interestedagents embedded in an arbitrary network topology. We as-sume that there is an unknown state of the world, which theagents are trying to learn based on their private informa-tion about the state and their observations of the actionsof their neighbors. We provide an explicit characterizationof the perfect Bayesian equilibria of this dynamic game.We establish conditions on network topologies and privateinformation structures under which agents can asymptoti-cally learn the state of the world.

Asu Ozdaglar, Ilan Lobel, Daron Acemoglu, MuntherDahlehMITasuman@mit.edu, lobel@mit.edu, daron@mit.edu,dahleh@mit.edu

MS18

Distributed Algorithms for Generalized NashGames and Their Convergence

We describe a distributed algorithm for a Nash equilibriumin a noncooperative game where each player’s objectivefunction and constraints both depend on the rival players’sstrategies.

Jong-Shi PangUniversity of Illinois at Urbana-Champaignjspang@uiuc.edu

Chiaoxong WangRensselaer Polytechnic Institutewangc@rpi.edu

MS18

Pricing in Oligopoly Markets for Perishable Prod-ucts: Learning and Loss of Efficiency

In this talk we present a model for dynamically pricing mul-tiple perishable products that sellers need to sell over a fi-nite time horizon (i.e. in this setting, each seller has a fixedinventory of several products that he/she needs to sell overa finite time horizon). We are considering an oligopolis-tic market and assume that sellers compete through pric-ing (Bertrand competition). Applications in mind includepricing airline tickets in the face of competitor airlines, aswell as selling seasonal products in the retail industry inthe presence of competitors. The goal of this work is toaddress the competitive aspect of the problem but also thepresence of demand uncertainty. In particular, we proposea model that uses ideas from quasi-variational inequalities(in order to address the aspect of competition), ideas fromrobust optimization as well as MPECs (in order to address”uncertainty” of the demand). Robust optimization allowsus to propose a model that is tractable and does not assumeany particular type of distribution for the uncertain param-eters of demand. We consider open and closed loop policiesthrough adjustable robust optimization. Furthermore, weconsider a setting where sellers learn their demand pricefunction parameters. Sellers only know that their demandbelongs in a parametric class of demand functions. In this

setting there are two levels of learning: i) sellers learningtheir demand through data and ii) trying to understandtheir competitors? policies as they collect more data onprices for them and their competitors as time progressesand the selling horizon unfolds. We use ideas from MPECsto study this enhanced model of joint pricing and demandlearning. (parts of this work are joint with S. Kachani, R.Lobel, D. Nguyen, A. Sood, C. Simon)

Georgia PerakisMITgeorgiap@mit.edu

MS18

Polynomial Stochastic Games Via Sum of SquaresOptimization

Stochastic games are an important class of games that gen-eralize Markov decision processes to game theoretic scenar-ios. We consider finite state two-player zero-sum stochasticgames over an infinite time horizon with discounted re-wards. The players are assumed to have infinite strategyspaces and the payoffs are assumed to be polynomials. Inthis paper we restrict our attention to a very special classof games for which the single-controller assumption holds.It is shown that minimax equilibria and optimal strategiesfor such games may be obtained via semidefinite program-ming.

Parikshit ShahMITpari@mit.edu

Pablo A. ParriloMassachusetts Institute of Technologyparrilo@MIT.EDU

MS19

Topology Optimization in Sheet Metal Design withMixed-Integer Programming

The design process of a multi-channel conduit involves atopology optimization in the first place. The question ishow to arrange the different channels so that certain de-sign goals such as minimum weight and/or maximum sta-bility are met. We present different mixed-integer linearprogramming formulations for this problem, theoretical re-sults, and numerical solutions for some test instances.

Armin FuegenschuhTU DarmstadtFB Mathematicsfuegenschuh@matheamtik.tu-darmstadt.de

Alexander MartinTU DarmstadtFB Mathematikmartin@mathematik.tu-darmstadt.de

MS19

Handling Manufacturing Constraints Using Dis-crete Optimization

Given a topology of a sheet metal profile, how can it beproduced when taking manufacturing restrictions into ac-count? We model the problem as a graph such that eachpossible way of production corresponds to a Steiner tree.The manufacturing restrictions can be modeled as addi-

90 OP08 Abstracts

tional restrictions such as on the diameter or the degree ofthe tree. We present a mixed-integer program including allthese constraints and develop new graph algorithms for itssolution.

Ute GuentherTU DarmstadtFB Mathematicsuguenther@mathematik.tu-darmstadt.de

Alexander MartinTU DarmstadtFB Mathematikmartin@mathematik.tu-darmstadt.de

MS19

New Forming Technologies for Sheet Metal

The processes linear flow splitting and linear bend splittingenable the production of branched profiles in integral stylemade of sheet metal without joining, lamination of materialor heating of the semi-finished product. This new formingtechnologies provides the opportunity to design new prod-uct classes with optimized mechanical properties. By afollowing forming process new multi-chambered structuresand integral stringer construction can be realized with thinwalled cross-sections made from steel of higher strength.

Jens RinglerTU DarmstadtFB Mechanical Engineeringringler@ptu.tu-darmstadt.de

Groche Peter, Vucic DragoslovTU-Darmstadtgroche@ptu.tu-darmstadt.de, vucic@ptu.tu-darmstadt.de

MS19

Product Properties as the Basis for Optimization

Product development can be seen as the optimization of in-ternal properties (e.g. geometrical properties) to fulfil de-sired external properties (e.g. deflection of a beam). Thisapproach needs precisely defined relations between exter-nal and internal properties based e.g. on physical models.These formalized interrelationships are used by subsequentmathematical optimization processes to compute and eval-uate new geometries. We demonstrate our method by de-signing a multi-channel profile, which can for instance beused as a conduit.

Martin WaeldeleTU DarmstadtProduct Development and Machine Elements (Mech.Eng.)waeldele@pmd.tu-darmstadt.de

Herbert BirkhoferTU Darmstadtbirkhofer@pmd.tu-darmstadt.de

MS20

Optimum Active Pricing for Communication Net-works with Multiple User Types and InformationAsymmetry

The talk will introduce a class of hierarchical games thatarises in pricing of services in communication networks

with a monopolistic service provider and a large populationof users of different types. The probability distribution ondifferent user types is common/public information, but theprecise type of a specific user is not necessarily known to allparties. As such the game falls in the class of games withincomplete information, and in our specific case what wehave is a problem of mechanism design within an uncertainenvironment and with asymmetric information. The ser-vice provider is a revenue maximizer, with his instrumentbeing the prices charged (for bandwidth) as a function ofthe information available to him. The individual users areutility maximizers, with bandwidth usage being their deci-sion variable. The congestion cost in their utility functionscreates a coupling between different users’ objective func-tions, which leads to a noncooperative game at the lower(users) level for which we adopt Nash or Bayesian equilib-rium. Solutions to these problems (at both the lower andthe upper levels) entail non-standard multi-level optimiza-tion problems. Indirect approaches to these optimizationproblems will be presented, and some asymptotics for largeagent-population models will be discussed. (This is basedon a joint work with Hongxia Shen.)

Tamer BasarUniversity of Illinois at Urbana-Champaigntbasar@control.csl.uiuc.edu

MS20

Game Theoretic Approaches for Wireless Spec-trum Sharing

Abstract not available at time of publication.

Randy BerryDept of Electrical Engineering and Computer ScienceNorthwester Universityrberry@ece.northwestern.edu

MS20

From Optimization Theory to High-Speed InternetAccess: An Overview of Power Control in Wirelessand DSL Networks

This is an overview talk about the mathematical chal-lenges and practical implications of optimization problemsin interference-limited communication systems, includingpower control in wireless cellular networks and spectrummanagement in DSL broadband access networks. We willorganize the wide range of results over the last 15 years inthis area, illustrate the optimization-theoretic aspect of theproblems, discuss the open problems in operational net-works today, and highlight the interactions between themathematics of convexity, algorithms, and games, and theengineering for the grande challenge of delivering high-speed communication access to as many users as possible.

Mung ChiangDept of Electrical EngineeringPrinceton Universitychiangm@princeton.edu

MS20

Optimization for Spectrum Management in Mul-tiuser Communication

Optimal spectrum management in a communication sys-tem with multiple interfering users and hostile jammersis a major engineering design issue that has received con-siderable attention in both the optimization and electrial

OP08 Abstracts 91

engineering communities. From the optimization perspec-tive, it provides a rich contemporary application contextfor innovative optimization, game theoretic, and economicmodeling research as well as rigorous analysis. In this talk,we present an introduction to this area, focussing on for-mulation, complexity, asymptotic strong duality and poly-nomial time approximation.

Zhi-Quan LuoUniverisity of MinnesotaMinneapolis, Minnesotaluozq@ece.umn.edu

MS21

Failure of Newton-Like Methods for Optimization

Global convergence analysis of unconstrained optimizationmethods usually involves making sure the Hessian approx-imation is bounded away from singularity. However, inpractice methods for regularizing Newton-like methods of-ten do bother with this issue. Our investigations into thebehavior of Newton-like methods when the Hessian approx-imation approaches singularity show that failure due tosingularity can occur only under very restricted circum-stances. These results shed new light on several methodsincluding the regularized Newton’s method, the modifiedCholesky factorization, and the Gauss-Newton method.

Richard H. ByrdUniversity of Coloradorichard@cs.colorado.edu

Daniel CrumlyDept. of Computer ScienceUniversity of Coloradodaniel.crumly@colorado.edu

MS21

Adaptive Cubic Regularisation Methods for Non-linear Optimization with Convex Constraints

The adaptive cubic overestimation algorithm described inCartis, Gould and Toint (2007) is adapted to the problemof minimizing a nonlinear, possibly nonconvex, smooth ob-jective function over a convex domain. Convergence tofirst-order critical points is shown under standard assump-tions, but without any Lipschitz continuity requirementon the Hessian of the objective. A worst-case complex-ity result for the Lipschitz continuous case is derived fora variant of the proposed method, which extends the bestknown bound for general unconstrained problems to non-linear problems with convex constraints. Some preliminarynumerical results are also presented.

Coralia CartisUniversity of EdinburghCoralia.Cartis@ed.ac.uk

Nicholas I. M. GouldUniversity of OxfordRutherford Appleton Laboratorynimg@comlab.ox.ac.uk

Philippe L. TointUniversity of Namurphilippe.toint@fundp.ac.be

MS21

Matrix-Free Methods for PDE-Constrained Opti-mization

Very large-scale nonlinear programming applications re-quire careful selection of the most efficient numerical tech-niques. Prominent examples include problems where theconstraints are defined by a discretized system of partialdifferential equations, such as shape optimization problemsin Navier-Stokes flows. In this talk we consider the po-tential for the application of state-of-the-art optimizationtechniques to problems of this type.

Frank E. CurtisCourant Institute of Mathematical SciencesNew York Universityfecurt@gmail.com

MS21

Parallel Optimization and the Toolkit for AdvancedOptimization

We begin by presenting information on the design and im-plementation of the Toolkit for Advanced Optimization(TAO), and how the reuse of common optimization compo-nents is facilitated within the framework. We then discussthe some of the algorithms bundled with TAO for solvingcomplementarity and optimization problems. Results forthese methods are given along with an indication of theirparallel performance.

Todd S. MunsonArgonne National LaboratoryMathematics and Computer Science Divisiontmunson@mcs.anl.gov

Jason SarichArgonne National Laboratorysarich@mcs.anl.gov

MS22

Applications of MPECs for Dynamic Optimizationof Chemical Processes

Switching conditions and nonsmooth models in the dy-namic optimization of chemical engineering systems can betreated through the formulation of differential variationalinequalities. In this talk we apply a temporal discretizationto these dynamic systems and reformulate the variationalinequalities to complementarity conditions and solved withNLP formulations for MPECs. Several chemical engineer-ing examples are presented that illustrate these concepts.

Lorenz T. BieglerCarnegie Mellon UniversityPittsburgh, USAbiegler@cmu.edu

B. BaumruckerCarnegie Mellon Universitybiegler@cmu.edu

MS22

Feedback Solutions for Nonlinear Optimal ControlProblems

Optimal closed-loop (feedback) controllers, like the classi-cal Linear Quadratic Regulator (LQR), are able to com-

92 OP08 Abstracts

pensate perturbations appearing in reality. Unfortunatelythese controllers are often designed for linear modells onlyand hence are not optimal if the dynamical system ap-pears nonlinearly. If these controllers are applied in a realprocess, the possibility of further data disturbances forcerecomputing the feedback control law in real-time to pre-serve stability and optimality, at least approximately. Forthis purpose, a new feedback method based on the para-metric sensitivity analysis of NLP-problems is suggested.The new optimal controller can be adapted within a fewnanoseconds on an typical personal computer.

Christof BueskensUniversity of BremenBremen, GermanyBueskens@math.uni-bremen.de

MS22

Optimal Control of Large Power Generating KiteSystems

We show how advanced dynamic optimization techniquesbased on Bock’s direct multiple shooting method can beused to treat a challenging application problem, namelythe periodic control of large, fast flying kite systems. Afteran outline of the technological idea we first show how toformulate the periodic optimal control problem for powergenerating kites, and how to estimate realistic model pa-rameters based on measurement data. Second, we discussseveral ways to control the kites in the presence of distur-bances, among them a periodic linear control, and modelpredictive control. This is joint work with Boris Houska,Andreas Ilzhoefer, Kenny Evers, Bart Struyven.

Moritz DiehlK.U.Leuvenmoritz.diehl@esat.kuleuven.be

MS22

Semi-Automatic Transition from Simulation to Op-timization

The talk concerns the development of mathematical meth-ods, algorithmic techniques and software tools for the tran-sition from simulation to optimization. The methodology isapplicable to all areas of scientific computing, where largescale governing equations involving discretized PDEs aretreated by custom made fixed point solvers. To exploitthe domain specific experience and expertise invested inthese simulation tools we propose to extend them in a semi-automated fashion. First they are augmented with adjointsolvers to obtain (reduced) derivatives and then this sensi-tivity information is immediately used to determine opti-mization corrections. In other words, rather than applyingan outer optimization loop we prefer the “one-shot” strat-egy of pursuing optimality simultaneously with the goalsof primal and adjoint feasibility. First results for aerody-namic shape optimization will be presented.

Nicolas R. GaugerHumboldt University BerlinFaculty of Mathematics and Natural Sciences IInicolas.gauger@dlr.de

MS23

Nested Approach for Solving Design OptimizationProblem

Our talk concerns a design optimization problem, where

the constraint is a state equation that can only be solvedby a typically rather slowly converging fixed point solver.This process can be augmented by a corresponding adjointsolver, and based on the resulting approximate reducedderivatives, also an optimization iteration, which actuallychanges the design. To coordinate the three iterative pro-cesses, we consider an augmented Lagrangian function thatshould be consistently reduced whatever combination of se-quence of primal, dual and optimization steps one chooses.This function depends on weighting coefficients which in-volve the primal and dual residuals and on the Lagrangian.The key question is the choice of the weighting coefficientsand the construction of the preconditioner in order to geta reasonable convergence rate of the coupled iteration. Inthis talk, we present theoretical results as well as some nu-merical results done by considering the Bratu equation onthe 2D unit square.

Adel Hamdi, Andreas GriewankHU Berlinadel.hamdi@math.hu-berlin.de,riewank@math.hu-berlin.de

MS23

An SQP Method for Semilinear Elliptic Opti-mal Control Problems with Nonlinear BoundaryControl-State Constraints

In this talk we will consider a family of optimal controlproblems governed by semilinear elliptic partial differentialequations (PDEs) with pointwise nonlinear control-stateinequality constraints. Problems with mixed control-stateconstraints are important as Lavrentiev-type regulariza-tions of pointwise state-constrained problems, but they arealso interesting in their own right. We will briefly reviewthe associated optimality conditions and regularity resultsfor Lagrange multipliers. Optimal control problems involv-ing semilinear PDEs can be efficiently solved using the se-quential quadratic programming (SQP) method, which isequivalent to a generalized Newton’s method. The localconvergence behavior of this method relies essentially onthe strong regularity of the first-order optimality system,i.e., on the Lipschitz continuous behavior of solutions to anauxiliary linear-quadratic optimal control problem. SuchLipschitz stability results and the local quadratic conver-gence of the SQP method applied to the original problemwill be discussed. Numerical examples will be used to il-lustrate our results.

Nataliya MetlaRICAMnataliya.metla@oeaw.ac.at

MS23

An Inexact SQP Method for Optimizing of a Sim-ulated Moving Bed Process

The Simulated Moving Bed process is an adsorption pro-cess for the separation of dissolved chemicals. It consistsof several cyclically connected adsorption columns. Bymeans of periodical switching of inflow and outflow portsbetween the columns, a counter-current movement of theadsorbent is simulated. When operated over a longer time,the process runs into a cyclic steady state (CSS). Desir-able is a CSS which is optimal with respect to operationalcosts and product specifications. This can be modelledas a PDE constrained optimization problem with period-icity constraint in time. An inexact SQP method is usedsolve the discretized optimization problem. Inspired form

OP08 Abstracts 93

so called Newton-Picard methods for calculation of theCSS, only low-rank approximations of the periodicity con-straint derivative are calculated, requiring only few direc-tional derivatives. An orthogonal basis of an approxima-tion to the eigenspace of the largest eigenvalues of the pe-riodicity constraint jacobian is simultaneously updated bya Subspace Iteration to yield the derivative directions.

Andreas PotschkaInterdisciplinary Center for Scientific ComputingUniversity of Heidelbergpotschka@iwr.uni-heidelberg.de

Hans Georg BockIWR, University of Heidelbergbock@iwr.uni-heidelberg.de

Moritz DiehlK.U.Leuvenmoritz.diehl@esat.kuleuven.be

Sebastian EngellUniversity of DortmundGermanysebastian.engell@bci.uni-dortmund.de

Ekatarina KostinaUniversity of Marburgkostina@mathematik.uni-marburg.de

Achim KuepperDept. of Biochemical and Chemical EngineeringUniversity of DortmundAchim.Kuepper@bci.uni-dortmund.de

Johannes P. SchloederIWR Universitat Heidelbergj.schloeder@iwr.uni-heidelberg.de

MS23

On a State-Constrained Optimal Control ProblemInvolving Nonlocal Radiation Interface Conditions

A state-constrained optimal control problem arising in thecontext of sublimation crystal growth is considered. Thenonlocal radiation interface conditions and the presence ofpointwise state-constraints constitute a major issue of thisproblem. The goal of this talk is twofold: Firstly, the nec-essary and sufficient optimality conditions associated withthe problem are discussed. Secondly, a Moreau-Yosida typeregularization is considered to cope with the weak regular-ity of the Lagrange multipliers. Optimality conditions forthe regularized problem are presented and the convergenceof the regularized solutions is shown.

Irwin YouseptTU-Berlinyousept@math.tu-berlin.de

Christian MeyerWIAS, Berlinmeyer@wias-berlin.de

MS24

A Backtracking Heuristic for Graph Coloring

The number of colors used by a greedy graph coloring al-gorithm is to a large extent determined by the order in

which the vertices are colored. We present a backtrack-ing correction algorithm that partially changes the effectsof the underlying vertex ordering by rearranging the map-ping of the colors. The backtracking heuristic is used inconjunction with a top level coloring algorithm to decreasethe number of colors in the graph.

Sanjukta BhowmickDepartment of Computer Science and EngineeringPennsylvania State Universitybhowmick@cse.psu.edu

MS24

Heuristics for the Linear Arrangement Problem

The linear arrangement minimization problem consists offinding a labeling or arrangement of the vertices of a graphthat minimizes the sum of the absolute values of the differ-ences between the labels of adjacent vertices. This is a well-known NP-hard problem that presents a challenge to solu-tion methods based on heuristic optimization. Many lineararrangement reduction algorithms have recently been de-veloped and applied to structural engineering, VLSI andsoftware testing. We undertake the development of dif-ferent heuristic procedures with the goal of uncoveringthe most effective designs to tackle this difficult but im-portant problem. Specifically, we consider the adaptationof constructive, local search, GRASP and Path Relinkingmethods for the linear arrangement minimization. We per-form computational experiments with previously reportedinstances to first study the effects of changes in criticalsearch parameters and then to compare the efficiency ofour proposal with previous solution procedures.

Rafael MartiUniversity of ValenciaValencia, Spainrafael.marti@uv.es

Abraham Duarte, JuanJose PantrigoUniversity Rey Juan Carlosabraham.duarte@urjc.es, juanjose.pantrigo@urjc.es

Vicente CamposUniversity of Valenciavicente.campos@uv.es

MS24

Minimal Arrangement of Clos Networks

Clos networks are switching matrices that are used in highfrequency transmissions. For a given matrix with N inputsand M outputs, these matrices are arranged in three stageseach of which is build up by so-called switches. Whereasthe size and number of switches in the first and third stageare basically determined by N and M the task is to findthe minimal number of switches in the middle stage. Howmany of these switches are necessary to guarantee routabil-ity is a long open question even for small sized matrices.By applying techniques from integer and combinatorial op-timization we are able to determine the minimal numberof switches for Clos networks with up to 32 inputs andoutputs.

Alexander MartinTU DarmstadtFB Mathematikmartin@mathematik.tu-darmstadt.de

94 OP08 Abstracts

Peter LietzTU Darmstadtlietz@mathematik.tu-darmstadt.de

MS24

0/1 Model for the Linear Arrangement Problem

The Linear Arrangement Problem consists of finding anordering of the nodes of a weighted graph on n nodes suchthat the sum of the weighted edge lengths is minimized.We report about the usefulness of a new modeling ap-proach within a branch-and-cut algorithm for solving Lin-ear Arrangement Problems to optimality. The key idea isto introduce binary variables dijk for 1 ≤ i < j ≤ n and1 ≤ k ≤ n − 1, where dijk = 1 if nodes i and j have dis-tance k. We present different strategies how the number ofof variables within this model can be reduced.

Hanna SeitzUniversity of HeidelbergHeidelberg, Germanyhanna.seitz@informatik.uni-heidelberg.de

MS25

On the Nullstellensatz Method for CombinatorialOptimization

Unlike linear models, systems of multivariate polynomialequations over the complex numbers can be easily used tomodel combinatorial problems. In this way, a problem isfeasible (e.g. a graph is 3-colorable, Hamiltonian, etc.) ifand only if a certain system of polynomial equations has acomplex solution. In the work of M. Laurent, J. Lasserreand P. Parrilo, Y.Nesterov, and others, optimization prob-lems which are modeled by a zero dimensional radical idealhave been shown to have a finite sequence of semidefiniteprograms that converge to the optimal solution. But forfeasibility problems (e.g., is G Hamiltonian?) the (com-plex) Hilbert Nullstellensatz gives a sequence of linear alge-bra problems that eventually decides for sure the property.In this talk we present theoretical and experimental resultsabout these sequences of linear algebra relaxations to thecombinatorial optimization problem. We show that thesize of the smallest Nullstellensatz linear algebra systemcertifying that there is no stable set of size larger than thestability number of the graph grows as fast as the stabilitynumber of the graph. We also show discuss this method asa practical way for detecting 3-colorability of graphs.

Jesus De LoeraUniversity of California, Davisdeloera@math.ucdavis.edu

MS25

Finding Low-Rank Matrices by Convex Optimiza-tion

In many applications, notions such as complexity or degreeof a model or design correspond to the rank of a matrix.Choosing the “simplest” model often results in a matrixrank minimization problem, which is NP-hard in general.This talk discusses convex relaxations based on semidef-inite programming, and covers recent results on guaran-teed minimum rank solutions to linear equalities via nu-clear norm minimization.

Maryam FazelUniversity of Washingtonmaryam@cds.caltech.edu

MS25

Semidefinite Programming with Matrix Variables

The talk describes progress with algorithms which take ad-vantage of matrix structure. They start symbolically withnoncommutative algebra and derive efficient expressionsfor the linear subproblem. Then they proceed with iter-ative numerical linear solvers.

William HeltonUniversity of California, San Diegohelton@math.ucsd.edu

MS25

Semidefinite Programming Approach for Polyno-mial Least Squares Problems

We consider solving polynomial least squares problems viasemidefinite programming relaxation. The degree of theobjective function, represented as a sum of positive andeven powers of polynomials, affects the computational ef-ficiency. We propose the methods to transform polyno-mial least squares problems to polynomial semidefinite pro-grams to reduce degrees of the polynomials. The efficiencyof solving the original polynomial least squares problemand the transformed polynomial semidefinite programs iscompared. Numerical results on selected polynomial leastsquares problems show better performance of the trans-formed polynomial semidefinite program.

Sunyoung KimEwha W. Universityskim1510@yahoo.com

Masakazu KojimaTokyo Institute of Technologykojima@is.titech.ac.jp

MS26

Intriguing Analogies Between the Edge and CentralPaths

Linear optimization consists of maximizing, or minimizing,a linear function over a domain defined by a set of linearinequalities. Simplex methods, which follow an edge-path,and the primal-dual interior point methods, which followthe central path, are currently the most computationallysuccessful algorithms. In this talk we highlight intriguinganalogies between the edge and central paths, and betweenthe diameter of a polytope and the largest possible totalcurvature of the associated central path.

Antone DezaDept. of Comp., Fac. of Engg., McMaster Univ. 1280Main St.West, Hamilton, Ontario L8S 4K1, CANADAdeza@mcmaster.ca

Tamas Terlaky, Feng Xie, Yuriy ZinchenkoMcMaster Universityterlaky@mcmaster, xief@mcmaster.ca,zinchen@mcmaster.ca

MS26

A Comparative Study of Notions of Curvature ofCentral Path in Linear Programming

The central path method is one of the most efficient in-

OP08 Abstracts 95

terior point methods to solve linear programs. Recently,several attempts have been made to study the geometry ofcentral path, particularly, the curvature of central path us-ing different notions of curvature. In this paper we presenta comparative study of various notions of curvature of cen-tral path in linear programming.

Masudur R. QuabiliUniversity of Michigan, Dearbornmrquabili@yahoo.com

MS26

Curvature of Central Path and ComputationalComplexity of Linear Programming

In this paper we present some new results to developbounds on the curvature of the central path of a linearprogram (LP), and use them to obtain upper and lowerbounds, in the form of curvature integral, on the iterationcomplexity of LP path following algorithms.

Renato C. MonteiroSch. of Indus & System Engg.Georgia Institute of Technologymonteiro@isye.gatech.edu

Jai N. SinghBarry Universityjsingh@mail.barry.edu

Takashi TsuchiyaThe Institute of Statistical Mathematicstsuchiya@sun312.ism.ac.jp

MS26

An Infor-mation Geometric Approach to Polynomial-TimeInterior-Point Algorithms: Complexity Bound ViaCurvature Integral

We study polynomial-time interior-point algorithms inview of information geometry. We consider informationgeometric structure for conic linear programs introducedby self-concordant barrier funtions, and develop a preciseiteration-complexity estimate based on an integral of cur-vature of the central trajectory in a rigorous differentialgeometrical sense. The theory has a surprising link to theexisting results on geometrical structures of the central tra-jectory for classical LP by Vavasis and Ye, and Monteiroand Tsuchiya.

Takashi TsuchiyaThe Institute of Statistical Mathematicstsuchiya@sun312.ism.ac.jp

Atsumi OharaOsaka University, Department of Systems Innovationohara@sys.es.osaka-u.ac.jp

MS27

Considerations in Evaluating Derivative-Free Methods for Simulation-Based OptimizationProblems

Derivative-free methods have emerged as invaluable forfinding solutions to simulation-based optimization prob-lems. However, one must consider that the goal in solv-ing such problems may not be to merely find the classical

”best” solution (i.e. the point that results in the small-est function value) but may also include finding a solutionwhich is robust with respect to the simulator. For exam-ple, it may be the case that answer A gives a smaller ob-jective function value, but that answer B is preferable inreal world situations. Moreover, efficiency is important be-cause the optimization is guided solely by function valueswhich require the solution of a simulation. In this talk, wewill examine these and other considerations that must betaken into account when optimization methods are evalu-ated for their usefulness and effectiveness. We will also dis-cuss appropriate metrics for making comparisons betweenmethods.

Genetha GraySandia National Laboratoriesgagray@sandia.gov

Monica L. Martinez-CanalesSandia National LabsComputational Sciences and Mathematics Researchmmarti7@sandia.gov

Katie FowlerClarkson Universitykfowler@clarkson.edu

MS27

Accelerating Active Set Methods and Extensionsto DFO.

In this talk we explore new strategies to accelerate activeset methods. We devote the second part of the talk todiscuss the implications for methods that do not make useof derivatives.

Jose Luis MoralesDepartamento de Matematicas. ITAM.moreales@guinness.ece.northwestern

Jorge NocedalNorthwestern Universitynocedal@ece.northwestern.edu

Giovanni FasanoUniversita di Romafasano@peano.dis.uniroma1.it

MS27

Benchmarking Algorithms for Derivative-Free Op-timization

Performance profiles have proven to be a useful tool forcomparing algorithms on large sets of problems in thederivative-based optimization setting. We introduce twonew complementary performance measures – relying onlyon function values – which address the different com-putational budgets and desired accuracy-levels found inderivative-free optimization. We illustrate the use ofthe new benchmarking procedures by comparing severalderivative-free optimization algorithms on a new set of testproblems.

Stefan M. WildCornell UniversitySchool of Operations Research &IEsmw58@cornell.edu

96 OP08 Abstracts

Jorge J. MoreArgonne National LaboratoryDiv of Math & Computer Sciencemore@mcs.anl.gov

MS27

Testing, Testing, 1, 2, 3—Do We Really KnowHow?

Many experts in areas ranging from system software todirect marketing assert that testing is a science. If theyare correct, it is fair to ask whether experts in non-derivative optimization are prepared to make definitivestatements about (i) which methods are the best choicefor various problem classes, and (ii) which implementa-tions are the most effective and reliable. Since getting non-controversial answers to these questions remains problem-atic, this talk will examine our current knowledge aboutthe computational properties and practical performanceof non-derivative optimization methods, and also considerwhether we can define sensible metrics to enhance futuretesting.

Margaret H. WrightNew York UniversityCourant Institute of Mathematical Sciencesmhw@cs.nyu.edu

MS28

An Adaptive Retrospective Trust-Region Algo-rithm for Stochastic Programming

Bastin et al. have recently proposed a variant of the classi-cal trust-region, called retrospective trust-region. Its mainingredient is that the trust-region radius update is decidedbased on the restropective ratio between the current it-erate and the previous one. In this talk, we exploit thisidea inside the adaptive trust-region method developed byBastin, Cirillo and Toint for nonlinear stochastic program-ming, also using this ratio when deciding the level of accu-racy of sample average approximations.

Fabian BastinUniversit de Montralbastin@iro.umontreal.ca

Vincent MalmedyUniversity of NamurBelgiumvincent.malmedy@fundp.ac.be

Melodie MouffeCERFACSmouffe@cerfacs.fr

Philippe L. TointThe University of NamurDepartment of Mathematicsphilippe.toint@fundp.ac.be

Dimitri TomanosUniversity of NamurBelgiumdimitri.tomanos@fundp.ac.be

MS28

Decomposition Schemes for Stochastic DVIs

A recent paper by Pang and Stewart (2007) provides acomprehensive introduction to differential variational in-equalities(DVI). We consider a stochastic generalization ofsuch problems, looking specifically at uncertainty in thecontrol problem within the DVI framework. Decomposi-tion schemes for such problems are discussed and somepreliminary algorithmic evidence is provided.

Maureen DoyleAssistant ProfessorNorthern Kentucky Universitydoylem3@nku.edu

Uday ShanbhagDepartment of Industrial and Enterprise SystemsEngineeringUniversity of Illinois at Urbana-Champaignudaybag@uiuc.edu

MS28

Stochastic Variational Inequalities: Models and Al-gorithms

We consider the class of variational inequalities resultingfrom coupled two-period stochastic Nash games and discusssome motivating applications. Existence statements areprovided in a variety of settings. Furthermore, we providea discussion of chance-constrained VIs, a relatively newclass of stochastic equilibrium problems. Some preliminaryalgorithmic efforts are discussed.

Uma RavatGraduate student, dept. of MathUIUCuravat1@yahoo.com

Uday ShanbhagDepartment of Industrial and Enterprise SystemsEngineeringUniversity of Illinois at Urbana-Champaignudaybag@uiuc.edu

MS28

Adaptive Precision Adjustment in Stochastic Non-linear Programming

We consider nonlinear stochastic programs and present anapproach for adaptively determining efficient sample sizesin sample average approximations. The approach uses rateof convergence and sampling error estimates to determinesample sizes for the next several iterations. The approachbalances computational cost of large sample sizes with ac-curacy of the sample averages. The approach is imple-mented using a rolling planning horizon and is illustratedwith applications from structural engineering design prob-lems.

Johannes O. RoysetAsst. Prof.Naval Postgraduate Schooljoroyset@nps.edu

MS29

Multigrid One-Shot Pseudo-Time Stepping

OP08 Abstracts 97

Method for Aerodynamic Shape Optimization

This talk presents a numerical method for aerodynamicshape optimization problems. It is based on simultane-ous pseudo-time stepping in which stationary states areobtained by solving the pseudo-stationary system of state,co-state and design equations. The main advantages ofthis method are that it blends in nicely with an existingpseudo-time stepping method for the state and the co-stateequations, that it requires no additional globalization tech-niques in the design space, and that a preconditioner canbe used for convergence acceleration which stems from thereduced SQP methods. To accelerate the convergence ofthe method further, ’optimization based’ multigrid strat-egy can be implemented.

Subhendu HazraFB IV-MathematicsUniversity of Trierhazra@uni-trier.de

MS29

Aerodynamic Shape Optimization of an ObliqueFlying Wing

Adjoint solvers for 3D computational fluid dynamics are ex-tremely useful for performing aerodynamic shape optimiza-tion of aircraft configurations. A new adjoint approach ispresented, where automatic differentiation is applied se-lectively to compute the partial derivatives present in theadjoint equations. This selective application of automaticdifferentiation is the central idea behind the ADjoint (au-tomatic differentiation adjoint) approach. An implementa-tion of this approach is used to optimize an oblique flyingwing subject to trim constraints.

Joaquim Martins, Charles MaderUniversity of Torontomartins@utias.utoronto.ca, martins@utias.utoronto.ca

MS29

Error Estimation and Sensitivity Analysis for FluidFlow Problems Involving Complex Geometries

The development of an adjoint method is presented for thecomputation of discretization error estimates and shapesensitivities of objective functions for aerodynamic designproblems. The adjoint method is implemented in con-junction with an embedded-boundary Cartesian mesh ap-proach. Several three-dimensional design examples, usingaircraft and spacecraft configurations, are used to demon-strate the robustness and efficiency of the resulting opti-mization framework.

Marian NemecELORET Corp.mnemec@mail.arc.nasa.gov

MS29

Toward Practical Application of Numerical Aero-dynamic Optimization

An aerodynamic component, such as a wing, must functioneffectively under a range of on- and off-design operatingconditions. Therefore, the associated aerodynamic opti-mization problem has many competing objectives. In thispresentation, an automated approach to such problems isdescribed and demonstrated. The basic idea is to treat theoff-design operating requirements as constraints while the

on-design conditions are assigned weights based on theirrelative importance. The resulting constrained multi-pointproblem is solved using a gradient-based Newton-Krylovalgorithm based on the discrete-adjoint approach.

David W. ZinggUniversity of Toronto Institute for Aerospace Studiesdwz@oddjob.utias.utoronto.edu

MS30

Optimal Control in Image Processing for BreastCancer Detection

Motivated by a problem in mammographic image process-ing, we develop a natural model for smooth image inter-polation. The model is based on a class of degenerateparabolic PDEs as well as an optimal control problem asso-ciated with the variable degeneracies. The control variableenters the diffusion coefficients of the PDE and, implic-itly, the solution space. We discuss spaces of discontinuousfunctions adapted to the PDE and the optimization prob-lem. We further demonstrate how a characterization interms of certain weighted and directional Sobolev spacescan be found which in turn enables us to obtain existenceresults for the simultaneous solution of the optimal controlproblem and the PDE.

Kristian BrediesCenter for Industrial MathematicsUniversity of Bremenkbredies@math.uni-bremen.de

MS30

Optimal Treatment Planning in RadiotherapyBased on Boltzmann Transport

Most dose calculation algorithms in clinical use rely onthe Fermi-Eyges theory of radiation which is insufficient atinhomogenities, e.g. void-like spaces like the lung. In con-trast, this work is based on a Boltzmann transport modelfor the radiation which accurately describes all physicalinteractions. Starting with this model we develop a directoptimization approach using adjoint equations. Several nu-merical results are presented.

Martin FrankTU KaiserslauternDepartment of Mathematicsfrank@mathematik.uni-kl.de

MS30

Constructing Vascular Systems from OptimalityCriteria

We create realistic vascular systems based on optimalityprinciples of theoretical physiology. Our technique takesas input the position and flow distribution of end points ofa vascular system. Optimization is driven by intravascularvolume minimization. Direct optimization of a vascularsystem, including topological changes, is used instead ofsimulating vessel growth. A good initial condition is foundby extracting key information from a previously optimizedmodel. This technique is used iteratively in a multi-levelapproach to create a more globally optimized vascular sys-tem. The generated models are similar to real data ac-quired from corrosion casts of a human liver.

Manfred GeorgWashington University in St. Louis

98 OP08 Abstracts

Department of Computer Science and Engineeringmgeorg@cse.wustl.edu

MS31

An Interior-Point Piecewise-Penalty Method forNonlinear Programming

We present an interior-point penalty method for nonlin-ear programming (NLP), where the merit function consistsof a piecewise linear penalty function (PLPF) and an �2-penalty function. The PLPF is defined by a set of penaltyparameters that correspond to break points of the PLPFand are updated at every iteration. The step directionis computed from an �2-regularized Newton system of thefirst-order equations of the barrier problem. In line search,a trial point is accepted if it provides a sufficient reductionin either the PLPF or the �2-penalty function. We establishstrong global as well as fast local convergence properties ofthe algorithm. Encouraging numerical results on CUTErtest set will be reported.

Lifeng ChenColumbia UniversityDepartment of Industrial Engineering and OperationsResearchlc2161@columbia.edu

Donald GoldfarbDepartment of Industrial Engineering and OperationsResearchColumbia Universitygold@ieor.columbia.edu

Andreas WaechterIBM T.J. Watson Research Centerandreasw@watson.ibm.com

MS31

Infeasibility Detection in Nonlinear Programming

One of the central questions in optimization is to determineif a problem is feasible. This question is important in itsown right since it may be difficult for a modeler to knowif the constraints imposed on a problem are compatible.Feasibility detection also plays a key algorithmic role inbranch and bound algorithms for mixed integer nonlinearoptimization. In that context, the problem has a specialstructure as it is known that only one constraint (or a groupof constraints) has been added to a problem that is knownto be feasible. In this talk we describe two new infeasibilitydetection techniques for nonlinear optimization based onpenalty methods.

Jorge NocedalDepartment of Electrical and Computer EngineeringNorthwestern Universitynocedal@eecs.northwestern.edu

Frank E. CurtisCourant Institute of Mathematical SciencesNew York Universityfecurt@gmail.com

Richard ByrdUniversity of Coloradorichard@research.cs.colorado.edu

MS31

An Adaptive Cubic Overestimation Funnel Algo-rithm for Constrained Optimization

In two recent papers, the authors have explored a noveladaptive cubic overstimation (ACO) algorithm for uncon-strained optimization (with C. Cartis) and a non-standardtrust-funnel algorithm for equality constrained problems.The first may be seen as a an alternative globalization tech-nique, with strong links with trust-region methods. Thesecond uses two simultaneous trust-regions (in the range-and null-spaces of the constraints, respectively) togetherwith a ”funnel” to enforce global convergence to first-orderstationary points. This talk will explore the natural cross-breed between those two proposals, in which two distinctcubic overestimators are adaptively computed in the range-and null-spaces of the constraints, in conjunction with afunnel and/or a filter.

Philippe L. TointThe University of NamurDepartment of Mathematicsphilippe.toint@fundp.ac.be

Nick I.M. GouldUniversity of OxfordOxford, UKnick.gould@comlab.ox.ac.uk

MS31

Warm Starting Interior-Point Methods in Branchand Bound

Interior-point methods are needed to solve continuous sub-problems arising in large-scale, nonlinear mixed-integerprogramming. We will propose a specialized penalty ap-proach for warm-starting interior methods inside branchand bound methods, where the continuous subproblemschange in a very structured way. We will outline ourpenalty approach, present a theoretical summary of theapproach, and present numerical results on sample prob-lems.

Richard WaltzUniversity of Southern Californiarwaltz@usc.edu

Fernando OrdonezUSC, Industrial and Systems Engineeringfordon@usc.edu

MS32

Application of Large Scale Parameter Estimationin the Aerospace Industry

Abstract not available at time of publication.

John BettsTechnical FellowThe Boeing Companyjbetts@thumper.rt.cs.boeing.com

MS32

Fast Online Computation for Linear and NonlinearModel Predictive Control in the kHz Range

The powerful feedback control technique of model predic-tive control (MPC) is already widely applied in industries

OP08 Abstracts 99

with slow complex processes, like chemicals, where the on-line solution of optimal control problems is possible. Withmore efficient computation, MPC promises to revolutionizethe way fast systems are controlled, e.g. in mechatronicsand automotive applications. In these industries, explicitMPC approaches are until now popular, which precom-pute all solutions and avoid online optimization, but sufferseverely from the curse of dimensionality and have a verylimited range of applicability. This talk focuses on thequestion how the most efficient methods for nonlinear op-timization in MPC, that have proven successful in chem-ical engineering applications, can be transferred to milliand microsecond applications. Several new issues pop up,e.g. how to efficiently solve online QPs, how to work withold system linearizations as long as possible, how to effi-ciently shift problem data and matrix factorizations, etc.Finally, we briefly present real-world and simulated MPCapplications from automotive, mechatronic, and power en-gineering. This talk is based on joint work with HansJoachim Ferreau, Leonard Wirsching, Lieboud Van DenBrouck, Andreas Ilzhoefer, Boris Houska.

Moritz DiehlK.U.Leuvenmoritz.diehl@esat.kuleuven.be

Hans Georg BockIWR, University of Heidelbergbock@iwr.uni-heidelberg.de

MS32

Feature-Based Sensitivity Analysis and ParameterEstimation for Dynamical Systems

Methods for the sensitivity analysis of “features” of non-linear dynamical systems are developed, in particular fea-tures of oscillatory systems (period, amplitude and phase).Then, the benefits of “feature-based” parameter estimationwill be demonstrated in the context of models from celland circadian biology. The resulting objective functionsare well behaved and the available experimental data lendsitself to the application of this technique. Finally, feature-based sensitivity analysis is applied for post-optimality sen-sitivity analysis.

Katharina WilkinsGraduate StudentMITschampel@mit.edu

Jared Toettcher, Bruce TidorMITtoettch@mit.edu, tidor@mit.edu

Paul I. BartonMassachusetts Institute of TechnologyDepartment of Chemical Engineeringpib@mit.edu

MS32

Frameworks for Direct Transcription

We discuss a general framework for the simultaneous col-location method for the solution of dynamic optimizationproblems. Problems in this class include parameter estima-tion, optimal control, multistage optimization and even op-timization with steady-state, distributed models. The talkexplores the role of fast NLP algorithms, problem decom-positions, NLP sensitivity and formulations to deal with

discrete decisions.

Larry BieglerCarnegie Mellon Universitylb01@andrew.cmu.edu

Victor ZavalaChemical EngineeringCarnegie Mellon Universityvzavala@andrew.cmu.edu

MS33

Large-Scale Parallel Algorithms for Inverse Prob-lems in Electrocardiology

In this work, we consider an inverse problem for the es-timation of the electrical properties of the heart tissue.We solve for the tissue excitability, a scalar spatial fieldthat determines the propagation of the action potentialin the myocardium. The Fitz-Hugh Nagumo model is anonlinear, two species reaction-diffusion PDE that modelsthe cardiac electrical activity. The inverse problem is for-mulated as a PDE-constrained optimization problem con-strained by the Fitz-Hugh Nagumo model. We use an L2-Tikhonov regularization for stability. We use a reducedspace approach and eliminate the state and the adjointvariables, and iterate in the inversion parameter space us-ing conjugate-gradient (CG) algorithm. We preconditionCG by a V-cycle multigrid scheme where the smootherin the multigrid scheme is one application of a reducedHessian preconditioner constructed using a appropriatelyselected Green’s function. We use operator splitting, apseudo-spectral discretization for diffusion, and a backwardEuler scheme to time-evolve the state and the adjoint equa-tions. We present fixed size and iso-granular scalability re-sults for problems with up to one billion variables on 1024processors on a Cray XT3 at the Pittsburgh Supercomput-ing Center.

George BirosUniversity of Pennsylvaniabiros@seas.upenn.edu

MS33

Domain Decomposition and Model Reduction forthe Optimal Control of Systems with Local Non-linearities

In several applications one is interested in the optimal con-trol of systems in which nonlinear partial differential equa-tions (PDEs) are posed on relatively small subdomains andare coupled to linear PDEs on surrounding, larger subdo-mains. The linear PDE solution on the surrounding subdo-mains needs to be computed accurately enough to provideacceptable boundary conditions for the nonlinear problemon the ‘inner’ subdomain. Our approach for solving suchproblems combine balanced truncation model reductionand optimization-ased domain decomposition to derive re-duced order models with guaranteed error bounds for thesePDE constrained optimization problems. Balanced trun-cation is applied to the linear subproblems with inputs andoutputs determined by the original in- and outputs as wellas the interface conditions between the subproblems. Opti-mization is applied to the reduced problems. The potentialof this approach is demonstrated for model problems mo-tivated by flow control and design applications.

Matthias HeinkenschlossRice University

100 OP08 Abstracts

Dept of Comp and Applied Mathheinken@rice.edu

Dan Sorensen, Kai SunRice Universitysorensen@rice.edu, kleinsun@rice.edu

MS33

The Smoothed Penalty Method for Inequality Con-strained Optimal Control Problems

We present an infinite dimensional version of a smoothed–penalty method for inequality constrained optimizationproblems. The algorithm has been introduced by Spel-lucci et. al. for finite–dimensional quadratic programmingproblems. In finite dimensions it is based on smooth ap-proximations to the exact l1-penalty function. We extendit to the infinite–dimensional setting and derive estimateson the control of smoothing and penalty parameter. Usingthese estimates convergence of the sequence of iterates isproven. We report numerical results for examples of opti-mal control problems for partial differential equations withpointwise state constraints.

Michael HertyUniversity of Kaiserslautern,Department of Mathematicsherty@mathematik.uni-kl.de

MS33

Solving State-Constrained Parabolic Optimal Con-trol Problems by Level-Set Based Shape Optimiza-tion Techniques

In the construction of algoritms for the numerical solutionof state constrained optimal control problems one usuallyhas to deal with the structural problem that multipliers aresingular measures which are concentrated on the boundaryof the active set of the constraint. Algorithms using ap-proximations of the multiplier, e.g., by approximate deltafunctions show a strong mesh depencence and can not eas-ily be transferred into the infinite dimensional setting. Hin-termueller and Ring used the idea of treating the active setas an unknown in a geometric shape space which needs tobe identified in such a way that the optimality system issatisfied. The identification problem was formulated as ashape optimization problem and the optimal shape wasfound using a level-set based technique, with a precondi-tioned shape gradient acting as the driving force for theshape variable. It turned out that the singular multiplier ispart of the obtainede driving force. It is incorpurated intothe speed function for the propagation of the level-set func-tion by using a standard extension proceedure thus posingno further numerical difficulties. This shape optimizationidea is now extended to the parabolic case. The active setthen becomes time-dependent and has to be identified ineach time-step. This means, the propagation of the level-set function takes place in the space-time cylinder and thedirect and the adjoint equations have to be solved on non-cylindrical domains. The approach is carried out testedfor the linear heat equation and for a non-linear coupledthermistor equation.

Wolfgang RingInstitut fuer MathematikUniversitaet Grazwolfgang.ring@kfunigraz.ac.at

MS34

Tuning Parameters for Prediction in RegularizedKernel Estimation

The Regularized Kernel Estimation (RKE) framework wasintroduced by Lu et al. (PNAS 2006) as a robust methodfor estimating dissimilarity measures between objects fromnoisy, incomplete, inconsistent and repetitious dissimilar-ity data. The RKE framework is useful in settings whereobject classification or clustering is desired but objects donot easily admit description by fixed length feature vec-tors. Instead, there is access to a source of noisy and in-complete dissimilarity information between objects, usu-ally described as a graph. RKE estimates a symmetricpositive semidefinite kernel matrix K which induces a realsquared distance admitting of an inner product. K is thesolution to an optimization problem with semidefinite con-straints that trades-off fit to the observed dissimilarity dataand a penalty of the form Jλrke(K) on the complexity ofK, where λrke is a non-negative regularization parameter.RKE uses the penalty Jλrke(K) = λrketr(K). We presentresults on methods for choosing values of the regularizationparameter λrke in the RKE problem, in particular, whenthe solution K is then used in a prediction task. We showthe CV2 method which selects regularization parametervalues in clustering and visualization applications. How-ever, based on a empirical study using protein sequencedata, we make the observation that similar clustering per-formance is achievable for a range of values of the RKEregularization parameter, indicating that precise tuning inthese applications might not be required. Based on thesame empirical study we make the observation that predic-tion performance, in contrast to clustering, may be highlydependent on the RKE regularization parameter. We pro-vide initial results on methods that jointly tune regulariza-tion parameters in both the RKE and prediction optimiza-tion problems.

Hector J. Corrada BravoDept of Computer ScienceUniversity of Wisconsin-Madisonhcorrada@cs.wisc.edu

Grace WahbaDepartment of StatisticsUniversity of Wisconsin-Madisonwahba@stat.wisc.edu

Stephen J. WrightUniversity of WisconsinDept. of Computer Sciencesswright@cs.wisc.edu

MS34

An Improved SDP-Based Distributed AlgorithmForgraph Realization with Applications to Molec-ular Conformation

We propose an algorithm for determining a proteinmolecule structure given sparse and noisy short-range in-teratom distances. Our divide-and-conquer algorithm re-cursively partitions the atoms into overlapping groups; es-timates via a semidefinite program and refines via gra-dient descent groups with fewer than 300 atoms; finallystitches overlapping groups to form the protein configu-ration. The algorithm is tested on molecules taken fromthe PDB database. A 13000-atom conformation problemis solved in 3 hours with an RMSD of 1.0A, given 30% of

OP08 Abstracts 101

the distances less than 6A.

Ngai-Hang Z. LeungDept of MathematicsNational University of Singaporedeutsixfive@gmail.com

Kim-Chuan TohDept of Mathematics and Singapore-MIT AllianceNational University of Singaporemattohkc@nus.edu.sg

MS34

Attacking the Nonconvexity of Graph EmbeddingDirectly, With Application to Molecular Confor-mation

We discuss an approach to graph embedding that leadsto a matrix optimization problem with nonconvex rankconstraints. Rather than solve a convex semidefinite re-laxation of the rank constraints we attack them directlyusing straightforward nonlinear programming techniques.Our approach has proven successful when applied to theembedding problem in molecular biology. We discuss thecomputational issues that arise, numerical experience withthe embedding problem, and alternative problem formula-tions based on nonconvex duality principles.

Robert M. LewisCollege of William and Maryrmlewi@wm.edu

MS34

A Brief History of Embedding

Graph embedding problems appear in many guises. In the1950s and 1960s, psychometricians and statisticians devel-oped multidimensional scaling, a collection of techniquesfor visualizing proximity data in low-dimensional Euclideanspaces. These techniques can be understood as algorithmsfor minimizing some measure of discrepancy between a setof Euclidean distance matrices and a set of dissimilaritymatrices. Modern applications of graph embedding, e.g.,inferring 3-dimensional molecular structure from informa-tion about interatomic distances, assigning locations to anetwork of sensors, various techniques for manifold learn-ing (nonlinear dimension reduction of multivariate data),can be formulated in the same manner.

Michael W. TrossetDepartment of Statistics, Indianamtrosset@indiana.edu

MS35

On the Road to Tractability: From Combinato-rial Optimization Via Copositive Programming toSDP-Based Approximation

Quite many combinatorial and some important non-convexcontinuous optimization problems admit a copositive repre-sentation, where the complexity of solving discrete, or non-convex, programs is shifted towards the complexity of sheerfeasibility. Using characterizations of copositivity, one ar-rives at various SDP-based approximations. However, notall of these are tractable with current technology. Thistalk addresses some approaches on which tractable SDPapproximations may be based, along with specific strate-gies to generate interesting test instances of intermediate

complexity.

Immanuel BomzeUniversity of Viennaimmanuel.bomze@univie.ac.at

MS35

On Semidefinite Programming Relaxations of theTravelling Salesman Problem

We review known results on semidefinite programming(SDP) relaxations of the traveling salesman problem(TSP). Subsequently, we introduce a new SDP relaxationof TSP based on an SDP relaxation of the quadratic assign-ment problem. We also present and analyse a randomizedrounding procedure that produces a tour from the optimalSDP solution. The relaxation and rounding procedure willbe illustrated on numerical examples.

Etienne De Klerk, Renata SotirovTilburg UniversityE.deKlerk@uvt.nl, r.sotirov@uvt.nl

MS35

Sensor Network Localization, Euclidean DistanceMatrix Completions, and Graph Realization

We study Semidefinite Programming, SDP, relaxations forSensor Network Localization, SNL, with anchors and withnoisy distance information. The main point of the paperis to view SNL as a (nearest) Euclidean Distance Matrix,EDM, completion problem and to show the advantages forusing this latter, well studied model. We first show thatthe current popular SDP relaxation is equivalent to knownrelaxations in the literature for EDM completions. Theexistence of anchors in the problem is not special. The setof anchors simply corresponds to a given fixed clique for thegraph of the EDM problem. We next propose a methodof projection when a large clique or a dense subgraph isidentified in the underlying graph. This projection reducesthe size, and improves the stability, of the relaxation.

Yichuan DingManagement Science and EngineeringStanford Universityy7ding@stanford.edu

Nathan KrislockDepartment of Combinatorics and OptimizationUniversity of Waterloongbkrislock@math.uwaterloo.ca

Jiawei QianCornell Universityjq35@cornell.edu

Henry WolkowiczDepartment of Combinatorics and OptimizationUniversity of Waterloohwolkowicz@uwaterloo.ca

MS35

Strong Duality and Stability in Conic Convex Pro-gramming

For nonlinear (minimization) optimization problems withoptimal value vP , weak duality holds in general, i.e. the op-timal value of the Lagrangian dual provides a lower bound,

102 OP08 Abstracts

vD ≤ vP . However, strong duality (i.e. vD = vP and vD isattained) requires a constraint qualification, CQ, e.g. theSlater (strict feasibility) CQ. In the absence of a CQ, thedual optimal value vD may be unattained and/or there canbe a positive duality gap vP − vD > 0. In addition, the(near) absence of a CQ results in numerical difficulties.We study conditions that guarantee a finite positive du-ality gap ∞ > vP − vD > 0. Necessary and sufficientconditions for a finite nonzero duality gap are given, and itis shown how these can be used to generate instances satis-fying this property. Numerical tests are included. We thenpresent an algorithm that solves in an efficient and stableway, feasible conic convex optimization problems, includ-ing those for which the Slater constraint qualification fails.In addition, we illustrate the close relation between strictcomplementarity and duality gaps.

Simon SchurrDept of Comb and OptUniversity of Waterloospschurr@math.uwaterloo.ca

Levent TuncelUniversity of WaterlooDept. of Combinatorics and Optimizationltuncel@math.uwaterloo.ca

Henry WolkowiczUniversity of WaterlooDept of Combinatorics & Optimhwolkowi@orion.math.uwaterloo.ca

MS36

Using Nonnegative Matrix and Tensor Factoriza-tions for Topic Detection and Tracking

The automated identification of semantic features is an im-portant goal for text mining applications. Through the useof low-rank nonnegative matrix factorization (NNMF), onecan retain natural data nonnegativity and thereby elim-inate the need for subtractive basis vector and encodingcalculations common to approaches such as principal com-ponent analysis for semantic feature abstraction. Withappropriate extensions, nonnegative tensor factorization(NNTF) can be used to exploit both temporal and semanticproximity and enable tracking of text-based objects froma variety of media. Exposing latent (unknown) commu-nication patterns within social networking environments,for example, would be possible with NNTF-based models.Demonstrations of NNMF and NNTF algorithms for topic(or discussion) detection and tracking using corpora suchas the Enron Email dataset will be presented.

Michael W. BerryUniversity of TennesseeDepartment of Electrical Engineering and ComputerScienceberry@eecs.utk.edu

Brett W. BaderSandia National LaboratoriesComputer Science and Informatics Departmentbwbader@sandia.gov

MS36

Effective Initializations for NMF algorithms

Nonnegative Matrix Factorization approximates a nonneg-ative matrix A ∈ �m×n, as A ≈WH, for two nonnegative

matrices W ∈ �m×k and H ∈ �k×n, and some k n.Existing algorithms typically start from random W and Hand iterate until convergence. This type of initializationtypically causes slow convergence, making the overall pro-cess quite expensive. In this talk we present alternative,typically more efficient, initialization techniques for NMFand its one sided variants, where there is no restriction inthe sign of one of the two factors. This presentation is jointwork of C. Boutsidis (RPI) and E. Gallopoulos (U. Patras).

Efstratios GallopoulosDepartment of Computer Engineering & InformaticsUniversity of Patras, Greecestratis@ceid.upatras.gr

Christos BoutsidisComputer Science DepartmentRennselaer Polytechnic Instituteboutsc@cs.rpi.edu

MS36

Nonnegative Matrix Factorizations and Clustering

Variations of the Nonnegative Matrix Factorization (NMF)are discussed for their application to clustering. We showhow interpreting the objective function of K-means as thatof a lower rank approximation with special constraints al-lows comparisons between various formulations of NMFand K-means and provides the insight to design new clus-tering algorithms. We discuss introduction of additionalconstraints such as sparsity and orthogonality on the fac-tors in the NMF objective function for the purpose of de-signing clustering algorithms based on NMF. The exper-imental results with synthetic and text data shows thatthese constrained NMF algorithms not only provide an al-ternative to K-means, but rather give much better andconsistent solutions to the clustering problem.

Haesun Park, Jingu KimGeorgia Institute of Technologyhpark@cc.gatech.edu, jingu@cc.gatech.edu

MS36

Greedy Algorithms and Complexity for Nonnega-tive Matrix Factorization

Nonnegative matrix factorization has become an importanttool in data mining. This talk will cover a class of algo-rithms called ‘greedy downdating’ and will show that theyare effective for simple models of text databases. We willalso show that NMF is an NP-hard problem in general.

Stephen A. VavasisUniversity of WaterlooDept of Combinatorics & Optimizationvavasis@math.uwaterloo.ca

Ali Ghodsi, Michael BiggsUniversity of Waterlooaghodsib@uwaterloo.ca, mike@doubleplum.net

MS37

A Subclass of Generating Set Search with Second-Order Convergence

We introduce a general subclass of generating set searchalgorithms, in which approximate second derivative infor-mation based only on previously sampled points is used to

OP08 Abstracts 103

construct directions for the algorithm to use. Specifically,if we have an approximate Hessian at each iteration, wechoose as directions its orthonormal eigenvectors and theirnegatives. We show that if the sequence of approximateHessians converges to the true Hessian in the limit, con-vergence to second-order stationary points can be achieved.We then discuss specific implementations for approximat-ing the Hessian in a way that can satisfy the hypotheses ofthe convergence theory. We conclude by presenting somenumerical results that verify our approach.

Lennart FrimannslundUniversity of BergenDepartment of Informaticslennart@ii.uib.no

Mark AbramsonAFITmark.abramson@afit.edu

Trond SteihaugInstitutt for InformatikkUniversitetet i BergenTrond.Steihaug@ii.uib.no

MS37

Advancements in the Development of HOPSPACK

HOPSPACK facilitates hybrid optimization using nativesource code of existing software. Two levels of parallelismare supported; both function evaluations and individualoptimizers may run asynchronously in parallel using a com-munal function value cache. Load balance is exploited tocreate efficient hybrids that share information, improvingoverall robustness. A simple interface allows users to dy-namically build custom combinations of supported opti-mizers. We will provide numerical results to demonstratethe overall effectiveness of parallel hybrid optimization.

Josh GriffinSandia National LaboratoriesComputational Science and Mathematics ResearchRecent developments in generating set search for n

Tamara G. KoldaSandia National Laboratoriestgkolda@sandia.gov

MS37

Sequential Penalty Approaches for Nonlinear Con-strained Optimization Without Derivatives

We consider the problem of minimizing a continuouslydifferentiable function subject to smooth nonlinear con-straints. We assume that the first order derivatives of theobjective function and of the constraints are not available.In this work we propose new globally convergent patternsearch and linsearch methods which are based on smoothsequential penalty functions. Numerical results on stan-dard test problems and the computational experience on apractical problem show that the approach is viable.

Giampaolo LiuzziConsiglio Nazionale delle Ricerche CNRIstituto di Analisi dei Sistemi e Informatica IASIliuzzi@dis.uniroma1.it

Stefano LucidiUniversity of Rome

lucidi@dis.uniroma1.it

Marco SciandroneUniversita degli Studi di Firenzesciandro@dsi.unifi.it

MS37

Recent Developments in Generating Set Search forNonlinear Programming

Recent experiments with generating set search (GSS) havemade clear that careful implementation choices can havean appreciable impact on the performance of GSS meth-ods, in terms of both reducing the number of function andconstraint evaluations required to find improvement andkeeping the computational overhead of the algorithm at aminimum. Furthermore, analysis provides useful insightswhen making such choices. In this talk we will discussfurther developments along this front.

Robert Michael LewisCollege of William and Marybuckaroo@math.wm.edu

Virginia J. TorczonCollege of William & MaryDepartment of Computer Scienceva@cs.wm.edu

MS38

Sampling and Integer Programming for Chance-Constrained Problems

Various applications in reliability and risk managementgive rise to optimization problems with constraints involv-ing random parameters which are required to be satisfiedwith a pre-specified probability threshold. There are twomain difficulties with such chance-constrained problems.First, checking feasibility of a given candidate solution ex-actly is, in general, impossible since this requires evalu-ating quantiles of random functions. Second, the feasibleregion induced by chance constraints is, in general, non-convex leading to severe optimization challenges. We ad-dress the first difficulty by solving approximate problemsbased on Monte Carlo samples of the random data. Wedemonstrate that this scheme can be used to yield bothfeasible solutions and statistical optimality bounds usingmodest sample sizes. Computational testing of the sam-pling approach indicates that it can be used to yield goodfeasible solutions and reasonable bounds on their quality.We address the second difficulty via integer programming.We perform a detailed polyhedral study of the convex hullof the set of feasible solutions of such problems, and de-velop families of strong valid inequalities. These inequali-ties, when used within a branch-and-cut scheme, serve tosignificantly improve relaxation bounds, and expedite con-vergence, hence allowing instances that are considerablylarger than have been considered before to be solved tooptimality. (Based on joint work with James Luedtke andGeorge L. Nemhauser)

Shabbir AhmedH. Milton Stewart School of Industrial & SystemsEngineeringGeorgia Institute of Technologysahmed@isye.gatech.edu

104 OP08 Abstracts

MS38

Optimization Problems with Multivariate Stochas-tic Ordering Constraints

We consider stochastic optimization problems where risk-aversion is expressed by a stochastic ordering constraint.The constraint requires that a random vector dependingon our decisions stochastically dominates a given bench-mark random vector. We identify a suitable multivariatestochastic order and describe its generator in terms of vonNeumann–Morgenstern utility functions. We develop nec-essary and sufficient conditions of optimality and dualityrelations for optimization problems with this constraint.Assuming convexity we show that the Lagrange multipli-ers corresponding to dominance constraints are elements ofthe generator of this order, thus refining and generalizingearlier results for optimization under univariate stochasticdominance constraints. Furthermore, we obtain necessaryconditions of optimality for non-convex problems under ad-ditional smoothness assumptions.

Darinka DentchevaDepartment of Mathematical SciencesStevens Institute of Technologydarinka.dentcheva@stevens.edu

MS38

Combinatorial Pattern Method for Probabilisti-cally Constrained Optimization Problems

I consider stochastic optimization problems containing ajoint probabilistic constraint with a random right-hand sidefollowing a multivariate probability distribution with fi-nite support. I propose a novel approach based on theextraction of combinatorial patterns that define the min-imal conditions to be satisfied for the joint probabilisticconstraint to hold. The combinatorial patterns take theform of conjunctions of literals and the probabilistic con-straint is replaced by a constraint on a disjunctive normalform. The approach allows the substitution of an MIP forthe original stochastic problem. Computational results willbe presented.

Miguel LejeuneDrexel UniversityDecision Sciences, LeBow College of BusinessMiguel.A.Lejeune@drexel.edu

MS38

Cutting Plane Methods for Optimization Problemswith Stochastic Dominance Constraints

For stochastic optimization problems with second orderstochastic dominance constraints we present two formu-lations involving small numbers of variables and exponen-tially many constraints: primal and dual. The dual formu-lation reveals connections between dominance constraints,generalized transportation problems, and the theory ofmeasures with given marginals. Both formulations leadto two classes of cutting plane methods. Convergence ofboth methods is proved in the case of finitely many events.Numerical results for a portfolio problem are provided.

Andrzej RuszczynskiRutgers UniversityDepartment of Management Science and InformationSystemsrusz@business.rutgers.edu

Gabor RudolfRUTCOR, Rutgers Universitygrudolf@rutcor.rutgers.edu

MS39

Formulations for Supersonic Design Optimization

State-of-the-art design of supersonic aircraft has relied oninverse design formulations. This is a difficult strategy be-cause realizable targets are not known in practice. Recentattempts to replace inverse design by direct design opti-mization attempt to remove the dependence on targets.However, direct optimization has unresolved problems re-lated both to physical modeling and optimization problemformulation; e.g., it is not clear what to optimize. In thispresentation, we discuss alternative optimization formula-tions and their consequences.

Natalia AlexandrovNASA Langley Research Centern.alexandrov@nasa.gov

MS39

Shape Optimization of Axisymmetric Bodies Sub-ject to Aerodynamic Heating and Ablation

A common approach for mitigating the heat load of bodiessubject to strong aerodynamic heating is through the useof ablative coatings. As the surface ablates the shape of thebody changes, altering the flow, aerodynamic forces, andheat loads on the body. We present a computational analy-sis and design optimization framework for aerodynamicallyheated structures that accounts for this transient nonlinearinteraction and the heat transfer through the body usinghigh-fidelity numerical models.

Micah HowardUnversity of Coloradomicah.howard@colorado.edu

Kurt MauteUniversity of Coloradokurt.maute@colorado.edu

MS39

Supersonic Aircraft Design: Challenges for Opti-mization

This presentation highlights the application of numericaloptimization to several problems in supersonic aircraft de-sign, including the shape optimization of configurationswith laminar flow and tailored boom signatures. Theseproblems pose difficulties for conventional gradient-basedoptimization due to their discontinuous behavior, the needfor high fidelity analysis, and the absence of efficiently- gen-erated sensitivity information. The talk will describe someof the techniques used to address these problems, includinggradient-free search methods and emerging multi-fidelitymodeling strategies.

Ilan Kroo, Dev RajnarayanStanford Universitykroo@desktopaero.com, dgorur@stanford.edu

Peter Sturdza, David RodriguezDesktop Aeronautics, Incsturdza@stanfordalumni.org,davidlrodriguez@stanfordalumni.org

OP08 Abstracts 105

Mathias WintzerDesktop Aeronautics, Inc.mwintzer@stanford.edu

MS39

Multifidelity Optimization Methods for SupersonicAircraft Design

Supersonic aircraft design aims to eliminate the efficiency,environmental, and performance barriers to practical su-personic cruise vehicles. The high computational costs ofhigh-fidelity supersonic aircraft simulations motivate meth-ods to significantly reduce the cost of design optimization.One avenue of interest is multifidelity methodology: us-ing multiple models with differing levels of accuracy andcomputational cost. This work will identify promising ap-proaches for incorporation of multifidelity models in super-sonic design.

Karen E. WillcoxMITkwillcox@MIT.EDU

Theresa RobinsonAerospace Computational Design LaboratoryMassachusetts Institute of Technologyrobinst@mit.edu

MS40

Optimization in Radiation Therapy

We give an overview of all aspects of treatment planning,including the large scale optimization problem, which issolved for each individual patient based on the geometryand clinical state of his or her disease. We end with a dis-cussion of multi-objective optimization, a current researchtopic in radiotherapy which addresses the inherent trade-offs (tumor coverage versus healthy tissue sparing) involvedin radiation delivery.

David CraftMassachusetts General Hospitaldcraft@PARTNERS.ORG

MS40

Control Policies for Off-Line Adaptive RadiationTherapy

Optimization-based planning of radiation treatments of-ten produces sharp dose gradients between tumors andhealthy tissue. Due to random shifts during treatment, sig-nificant differences between the “optimized” plan and theactual dose can occur. Radiation is delivered as a seriesof small daily fractions, and we exploit the dynamic na-ture of treatment and information gathering by adaptingthe plan to fraction-to-fraction variations measured duringa patient’s treatment course within a DP framework andusing Bayesian updating.

Marina A. EpelmanUniversity of MichiganIndustrial and Operations Engineeringmepelman@umich.edu

Mustafa Sir, Stephen PollockDepartment of Industrial and Operations EngineeringThe University of Michiganmsir@umich.edu, pollock@umich.edu

MS40

Optimal Multileaf Collimator Leaf Sequencing inIMRT Treatment Planning

Optimized intensity profiles should be decomposed into de-liverable apertures and corresponding intensities so thattotal radiation therapy treatment time is minimized. Wedevelop the first exact algorithm capable of solving real-world problem instances to optimality (or to within prov-ably small optimality gaps) within practicable computa-tional limits, using a combination of integer programmingdecomposition and combinatorial search techniques. Wedemonstrate the efficacy of our approach on a set of 25clinical test instances.

Z. Caner Taskin, J. Cole SmithUniversity of Floridataskin@ufl.edu, cole@ise.ufl.edu

Edwin RomeijnDepartment of Industrial and Systems EngineeringUniversity of Floridaromeijn@ise.ufl.edu

James F. DempseyUniversity of Floridadempsey@ufl.edu

MS40

Specifying Dose Distribution Requirements for theRobust IMRT Treatment

Radiation therapy is a dominant modality in treating var-ious cancers. IMRT, its high-precision counterpart, is astate-of-the-art tool for this type of treatment. We in-vestigate the possibility of including the dose distribu-tion prescription (specified by the so-called dose-volumehistograms) within the robust IMRT treatment planningframework -the approach that allows to minimize the neg-ative impact of the inherent uncertainties- and relate thisquestion to the classical problem of moments.

Yuriy ZinchenkoMcMaster Universityyzinchen@optserv.cas.mcmaster.ca

MS41

Differential-Geometric Foundations of EigenvalueAlgorithms

The formulation of the extreme symmetric eigenvalue prob-lem as an optimization problem on a nonlinear mani-fold opens avenues for using several recently proposeddifferential-geometric optimization methods. We presenta general theory of Newton, trust-region, and conjugate-gradient methods on Riemannian manifolds, and we showhow these abstract algorithms yield concrete, competitivenumerical algorithms for the symmetric eigenvalue prob-lems, some of which shed a new light on the convergencebehavior of certain classical algorithms.

Pierre-Antoine AbsilUniversite catholique de LouvainBelgiumabsil@inma.ucl.ac.be

106 OP08 Abstracts

MS41

An Implicit Riemannian Trust-Region Method

We propose and analyze an “implicit” trust-region methodin the general setting of Riemannian optimization. Themethod is implicit in that the trust-region is defined as asuperlevel set of the ρ ratio of the actual over predicteddecrease in the objective function. This approach replacesthe trust-region heuristic with a meaningful performancemeasure and abandons the classical accept/reject mecha-nism to improve efficiency. The new method inherits theconvergence properties of the generic Riemannian trust-region method. Improved efficiency is demonstrated on theproblem of computing extreme eigenspaces of a symmetricdefinite matrix pencil.

Christopher G. BakerSchool of Computational ScienceThe Florida State University, USAcbaker@scs.fsu.edu

Pierre-Antoine AbsilUniversite catholique de LouvainBelgiumabsil@inma.ucl.ac.be

Kyle A. GallivanFlorida State Universitygallivan@scs.fsu.edu

MS41

Direct Search Methods Over Manifolds

We’ll examine how direct search methods can be employedover manifolds. Our main effort will be devoted to devel-oping pullback procedures for the C2 and C1 Riemannianmanifold cases using geodesics and the implicit functionfunction theorem. This allows us to redefine our prob-lem as an equivalent one in some Euclidean space Rn foran n-dimensional manifold. Applications to equality con-strained problems. We’ll also briefly examine the Lipschitzmanifold case.

David W. DreisigmeyerLANLdreisigm@lanl.gov

MS41

Higher-Order Tensors: Best Rank ApproximationAlgorithms

Higher-order tensors are generalizations of matrices in thesame way as matrices are generalizations of vectors. Theyhave various application areas, such as biomedical engi-neering, image processing, scientific computing, and signalprocessing. Contrary to the matrix case, the best rank-(R1, R2, . . . , RN ) approximation of tensors cannot be ob-tained in a straightforward way. In this talk, we presentthe higher-order orthogonal iterations algorithm and derivetwo new algorithms that solve this problem, based on thetrust-region and conjugate gradient methods on manifolds.We touch on some of the applications.

Mariya Ishteva

K.U.Leuven, ESAT/SCDLeuven, BelgiumMariya.Ishteva@esat.kuleuven.be

Lieven De Lathauwer

K.U.Leuven, ESAT/SCD andSubgroup Science & Technology, Campus Kortrijklieven.delathauwer@kuleuven-kortrijk.be

Pierre-Antoine AbsilUniversite catholique de LouvainBelgiumabsil@inma.ucl.ac.be

Sabine Van HuffelK.U.Leuven, Belgiumsabine.vanhuffel@esat.kuleuven.be

MS42

Multilevel Semismooth Newton Methods for Elas-tic Contact Problems

We consider the application of semismooth Newton meth-ods to the solution of elastic contact problems. We showthat for a regularized problem the convergence is super-linear. Moreover we present an error estimate dependingon the regularization parameter. We show that multilevelmethods can be applied to solve the semismooth Newtonmethod and prove mesh-independent convergence of themultilevel method. Finally, we present numerical results.

Michael UlbrichTechnical University of MunichChair of Mathematical Optimizationmulbrich@ma.tum.de

Stefan UlbrichTechnische Universitaet DarmstadtFachbereich Mathematikulbrich@mathematik.tu-darmstadt.de

MS42

Biofilm Characterization Using Large Scale Opti-mization

Biofilms occur in aqueous systems ranging from water dis-tribution networks to human physiology. We use level setmethods driven by convection for the interface transportand diffusion-reaction dynamics for the nutrient consump-tion to predict biomass behavior. An inverse problem isformulated to calibrate initial conditions and reaction co-efficients by reconciling the differences of experimental ob-servations and numerical predictions. The implementationuses C++ abstraction concepts to efficiently implement theforward and adjoint equations.

Bart G. Van Bloemen Waanders, Judy HillSandia National Laboratoriesbartv@sandia.gov, jhill@sandia.gov

Kevin LongTexas Tech Universitykevin.long@ttu.edu

MS42

Solving the Trust-Region Subproblem Using Mul-tilevel Techniques

We propose a new technique to be used along with multi-level methods that solves the trust-region subproblem byapplying a multilevel version of the Mor-Sorensen method.The main advantage of this approach is to be able to findsecond-order solutions to the minimization problem for 3D-

OP08 Abstracts 107

problems and large scale discretizations. We present herethe new method, some numerical results and possible fu-ture discussions.

Melissa WeberUinversity of NamurBelgiummwm@math.fundp.ac.be

Dimitri TomanosFUNDPNamur, Belgiumdtom@math.fundp.ac.be

Philippe L. TointThe University of NamurDepartment of Mathematicsphilippe.toint@fundp.ac.be

MS42

Adaptive Multilevel Inexact SQP-Methods forPDE-Constrained Optimization

We present a class of adaptive multilevel inexact SQP-methods for the solution of optimization problems gov-erned by nonlinear PDEs. Starting with a coarse FE-discretization of the underlying optimization problem wecombine an efficient trust-region SQP-method with an im-plementable adaptive refinement strategy based on esti-mators. The algorithm uses implementable accuracy re-quirements for the inexactness in iterative linear equationsolves. We prove global convergence to a first-order opti-mality point of the infinite-dimensional problem. Numeri-cal results are presented.

Jan Carsten ZiemsTechnische Universitat Darmstadt, Department ofMathematicsResearch Group Nonlinear Optimizationziems@mathematik.tu-darmstadt.de

Stefan UlbrichTechnische Universitaet DarmstadtFachbereich Mathematikulbrich@mathematik.tu-darmstadt.de

MS43

PDE-Constrained Optimization Problems and theChallenge of Finding Good Preconditioners

The nature of the quadratic sub-problems within PDE-constrained optimization problems means that iterativemethods are frequently used to solve the resulting saddle-point systems. By exploiting the very specific block struc-ture for several classes of such problems, we will show thatefficient and effective preconditioners can be formed. Thesensitivity of the quality of the preconditioner with respectto the regularization parameter in the problem will also bediscussed.

Sue DollarRutherford Appleton LaboratoryS.Dollar@rl.ac.uk

Nick GouldOxford UniversityRutherford Appleton Laboratorynick.gould@comlab.ox.ac.uk

Tyrone Rees, Andy WathenOxford Universitytyrone.rees@comlab.ox.ac.uk,andy.wathen@comlab.ox.ac.uk

MS43

Preconditioned Iterative Methods for GeneralizedSaddle Point Problems

We discuss the formulation and analysis of preconditionediterative methods for the solution of generalized saddle-point problems. We focus on those characteristics ofsaddle-point problems that are peculiar to interior meth-ods for general nonlinear optimization, such as inertia de-tection, approximate preconditioning and the treatment ofinherent ill-conditioning.

Philip E. GillUniversity of California, San DiegoDepartment of Mathematicspgill@ucsd.edu

MS43

An Overview of Iterative Solvers for Saddle PointSystems

In this talk I provide an overview of iterative methods forsolving saddle point (KKT) linear systems. We focus onpreconditioned Krylov subspace iterations with block pre-conditioners. Issues such as how to exploit the structure ofthe problem and how to effectively approximate the primaland dual Schur complements are to be discussed. Spectralanalysis of preconditioned matrices is provided and widelyused preconditioning techniques are described, along witha few numerical examples.

Chen GreifUniversity of British ColumbiaCanadagreif@cs.ubc.ca

MS43

Preconditioners for Semidefinite Programming

Semidefinite programming has become a valuable paradigmwhose practical impact is mainly limited by the ill-conditioned large dense systems of linear equations thatarise when implementing primal-dual interior-point meth-ods. We propose preconditioners for solving these systemsby iterative methods.

Chen GreifUniversity of British ColumbiaCanadagreif@cs.ubc.ca

Ming GuUniversity of California, BerkeleyMathematics Departmentmgu@math.berkeley.edu

Michael L. OvertonNew York UniversityCourant Instit. of Math. Sci.overton@cs.nyu.edu

108 OP08 Abstracts

MS44

Detection of 16-QAM Signaling in MIMO Channels

We develop a computationally efficient approximation ofthe maximum likelihood (ML) detector for 16 quadratureamplitude modulation in multiple-input multiple-output(MIMO) systems. The detector is based on solving aconvex relaxation of the ML problem by an affine-scalingcyclic Barzila-Borwein method for box constrained relax-ation problem. Simulation results show that this proposedapproach outperforms the conventional decorrelator detec-tors. Moreover, the complexity of the proposed approachis much less than that of other detectors.

Soonchul ParkKyungpook National Universityscp@knu.ac.kr

Hongchao ZhangUniversity of Minnesotahozhang@ima.umn.edu

William HagerUniversity of Floridahager@math.ufl.edu

Dong-Seog HanKyungpook National Universitydshan@ee.knu.ac.kr

MS44

An Ellipsoidal Branch and Bound Algorithm forGlobal Optimization

A branch and bound algorithm is developed for global op-timization. Branching in the algorithm is accomplished byellipsoidal bisections while bounds are obtained by com-puting the best linear underestimate for the concave partof the objective function restricted to an ellipsoid. An it-erative approach for solving convex relaxations of the orig-inal problem is developed which is based on successive ballapproximations to the original set. This algorithm is a gen-eralization an earlier scheme of Lin and Han. Numericalexperiments are reported.

Dzung Phan, William HagerUniversity of Floridadungphan@math.ufl.edu, hager@math.ufl.edu

MS44

Multilevel Algorithms For Linear Ordering Prob-lems

Linear ordering problems appear in many applications oflarge sparse matrix computation, VLSI design, biologi-cal applications, graph drawing, etc. Many heuristic al-gorithms (e.g., Spectral Sequencing, Optimally OrientedDecomposition Tree, Multilevel based, Simulated Anneal-ing, Genetic Hillclimbing, etc.) were developed in orderto achieve near optimal solution. We present a generalframework of linear time multilevel heuristic algorithms(MA) especially designed for linear ordering problems. Wedemonstrate how the building blocks of the general MAcan be used in various ways to make it suitable for solv-ing different functionals. We show how the bandwidth of agraph can be approximated by a continuation approach inwhich a sequence of minimum p-sum solvers are embedded

with progressively larger p.

Ilya SafroArgonne National Laboratorysafro@mcs.anl.gov

Dorit Ron, Achi BrandtThe Weizmann Institute of Sciencedorit.ron@weizmann.ac.il, achi.brandt@weizmann.ac.il

MS44

Quadratic Programming Techiniques for GraphPartitioning

In this talk, we are going to present quadraticprogramming-based block exchange techniques for graphpartitioning. Our numerical experiments indicate thesetechniques may yield a significant improvement in the par-tition quality.

Hongchao ZhangUniversity of Minnesotahozhang@ima.umn.edu

Soonchul ParkKyungpook National Universityscp@knu.ac.kr

William HagerUniversity of Floridahager@math.ufl.edu

MS45

CSDP: A Parallel Implementation of a Primal-DualMethod for SDP.

CSDP is a subroutine library and stand-alone solver forsemidefinite programming problems. CSDP is an opensource software package that has been published throughthe COIN-OR repository. This talk will focus on recent im-provements and future plans for CSDP including CSDP’suse of OpenMP on shared memory parallel systems. Com-putational results will be presented.

Brian BorchersDepartment of MathematicsNew Mexico Techborchers@nmt.edu

MS45

The SDPA Project: Solving Large-Scale Semidefi-nite Programs

In 1995, we started the SDPA Project aimed for solv-ing large-scale SDPs with numerical stability and accu-racy. The SDPA (SemiDefinite Programming Algorithm)is a C ++ implementation of a Mehrotra-type primal-dualpredictor-corrector interior-point method for solving thestandard form SDP and its dual. In this talk, we show somespecial features and future plans of the SDPA Project.

Kaisuki FujisawaDepartment of Industrial and Systems EngineeringChuo Universityfujisawa@indsys.chuo-u.ac.jp

Mituhiro FukudaTokyo Institute of Technology

OP08 Abstracts 109

Global Edge Institutemituhiro@is.titech.ac.jp

Masakazu KojimaTokyo Institute of Technologykojima@is.titech.ac.jp

Kazuhide NakataTokyo Institute of TechnologyDepartment of Industrial Engineering and Managementknakata@me.titech.ac.jp

Maho NakataThe Institute of Physical and Chemical Researchmaho@riken.jp

Makoto YamashitaKanagawa UniversityDepartment of Industrial Management and Sciencemakoto.yamashita@ie.kanagawa-u.ac.jp

MS45

Reimplementing SeDuMi: A Progress Report

SeDuMi was a Matlab based solver for optimization oversymmetric cones. To overcome various difficulties withMatlab we started to reimplement it using Python in late2007. In this talk we present our progress about this soft-ware challenge.

Imre PolikMcMaster UniversitySchool of Computational Engineering and Scienceimre.polik@gmail.com

Tams TerlakyMcMaster Universityterlaky@mcmaster.ca

MS45

Computational Experiences in Solving Large-ScaleSDP

We report our computational experiences on solving largescale SDPs via a primal-dual interior-point method forwhich the linear system at each iteration is solved by apreconditioned iterative method. We tested our algorithmson large scale SDPs from relaxation of combinatorial anddistance geometry problems, as well as nearest correlationmatrix problems in statistics. We also discuss the construc-tion of preconditioners and related computational issues forthe linear systems.

Kim-Chuan TohDepartment of Mathematics and Singapore-MIT AllianceNational University of Singaporemattohkc@nus.edu.sg

MS46

A Large-Update Infeasible Interior-Point Algo-rithm Based on the Logarithmic Barrier Functionfor Linear Optimization

Recently an O(n) infeasible full-Newton step interior-pointmethod was presented during which the iterates move ina small neighborhood (the region of quadratical conver-gence) of the central path of perturbed problems. We in-

troduce a long-step version of the algorithm. So the iteratesmay temporarily get far from the central path of perturbedproblems. Using a few damped centering steps we returnthem to the central path corresponding to the new valueof the barrier parameter.

Alireza AsadiTU Delfta.asadi@ewi.tudelft.nl

Cornelis RoosDelft University and Technologyc.roos@tudelft.nl

MS46

A New Search Direction for Self-Dual EmbeddedSemidefinite Optimization

In the literature on interior-point methods for semidefiniteoptimization, one key point is the need for well definedsearch directions, with blocks (in the direction) correspond-ing to symmetric matrices being symmetric. In the talk,a new search direction is proposed; the idea underlyingis to force these blocks to be symmetric by using linearconstraints. Primary numerical test shows that to someextend our new search direction is comparable with theNesterov-Todd direction.

Guoyong Gu, Kees RoosDelft University of Technologyg.gu@tudelft.nl, c.roos@tudelft.nl

MS46

Superlinear Convergence of an Infeasible-Interior-Point Method for Linear Optimization

Recently a primal-dual infeasible interior-point algorithmhas been proposed for linear optimization that uses onlyfull Newton steps. The iteration bound of this algorithmcoincides with the best known bound for infeasible interior-point algorithms. Each iteration of the algorithm consistsof a so-called feasibility step and some (usual) centeringsteps. In this paper we present a slightly different algo-rithm and we prove that the algorithm is Q-superlinearlyconvergent, while the complexity is the same as before.

Hossein MansouriTU DelftH.Mansouri@tudelft.nl

Maryam ZangiabadiDelft University of Technologym.zangiabadi@tudelft.nl

Cornelis RoosDelft University and Technologyc.roos@tudelft.nl

MS46

A New Primal-Dual Infeasible Interior-Point Algo-rithm for Second-Order Cone Optimization

We present a primal-dual infeasible interior-point algo-rithm for second-order conic optimization. It generalizesa recently published algorithm for linear optimization. Itis proven that the number of iterations of the algorithm isbounded by O(Nlog(N/ε), which coincides with the well-known best iteration bound for such algorithms. Here N

110 OP08 Abstracts

stands for number of second order cones in the problemformulation and ε for the desired accuracy.

Maryam ZangiabadiTU DelftM.Zangiabadi@tudelft.nl

Hossein MansouriDelft University of TechnologyH.Mansouri@tudelft.nl

Cornelis RoosDelft University and Technologyc.roos@tudelft.nl

MS47

Set-Semidefinite Optimization and Its Order Struc-ture.

We introduce set-semidefinite optimization as a new field ofvector optimization. We study vector-valued optimizationproblems having an inequality constraint with a specialpartial order in the space of linear maps. This order con-siders quadratic forms being non-negative on a set K. Infinite dimensions one obtains for K = Rn semidefinite andfor K = Rn

+ copositive optimization problems. For the as-sociated ordering cone calculation rules, characterizationsand results on the dual and on the interior are presented.

Gabriele EichfelderDepartment of MathematicsUniversity of Erlangen-NuernbergGabriele.Eichfelder@am.uni-erlangen.de

Johannes JahnDepartment of MathematicsUniversity of Erlangen-Nurembergjahn@am.uni-erlangen.de

MS47

Set-Valued Duality in Vector and Set Optimization.

We present a duality scheme for set-valued function that isbased on a new notion of affine minorants. Concepts likeproperness, convexity, sublinearity, indicator and supportfunctions, conjugates, inf-convolution and result like bicon-jugation and Fenchel–Rockafellar duality theorems are es-tablished within the new framework. Proofs do not rely onthe corresponding scalar theory, but many results can begiven an equivalent formulation for a family of scalar prob-lems. We apply the theory to linear vector optimizationproblems and to set-valued convex risk measures.

Andreas H. HamelDepartment of Operations Research and FinancialEngineering, Princeton Universityahamel@princeton.edu

MS47

An Existence Result for Equilibrium ProblemsWith Some Surjectivity Consequences

We present conditions for existence of solutions of equilib-rium problems, which are sufficient in finite dimensionalspaces, without making any monotonicity assumption onthe bifunction which defines the problem. As a conse-quence we establish surjectivity of set-valued operators ofthe form T + λI, with λ > 0, where T satisfies a property

weaker than monotonicity, which we call pre-monotonicity.We study next the notion of maximal pre-monotonicity. Fi-nally we adapt our condition for non-convex optimizationproblems, obtaining as a by-product an alternative proofof Frank-Wolfe’s Theorem.

Alfredo N. IusemIMPA, Rio de Janeiroiusp@impa.br

Wilfredo SosaInstituto De Matematica y Ciencias Afinessosa@uni.edu.pe

MS47

Optimality Conditions, Duality and Penalty Ap-proach in Set-Semidefinite Optimization

Set-semidefinite optimization is a new unified approach invector optimization covering semidefinite and copositiveoptimization and optimization with second-order optimal-ity conditions as constraints. For this general problem classwe give necessary and sufficient optimality conditions aswell as duality results. A penalty approach is presentedfor the treatment of the special quadratic constraint aris-ing in set-semidefinite optimization.

Gabriele Eichfelder, Johannes JahnDepartment of MathematicsUniversity of Erlangen-NurembergGabriele.Eichfelder@am.uni-erlangen.de,jahn@am.uni-erlangen.de

MS48

Newton Methods for Generalized Nash Equilib-rium Problems

In the generalized Nash equilibrium problem both the ob-jective function and the feasible set of each player may de-pend on the other players’ strategies. Although this equi-librium problem is an important modeling tool its use islimited by its analytical complexity. We therefore considerseveral Newton methods, analyze their features and com-pare their range of applicability. In particular, we addressthe issue of the non local uniqueness of the solutions thatcan cause severe difficulties.

Andreas FischerDresden University of TechnologyInstitute of Numerical MathematicsAndreas.Fischer@tu-dresden.de

Francisco FacchineiUniversita di Roma ”La Sapienza”Roma, Italyfacchinei@dis.uniroma1.it

Veronica PiccialliUniversita’ di Roma la SapienzaDipartimento di Informatica e Sistemisticapiccialli@dis.uniroma1.it

MS48

On the Numerical Performance of an Interior PointMethod for Complementarity Problems

We discuss the numerical performance of a new interiorpoint method for solving linear complementarity problems.

OP08 Abstracts 111

The algorithm uses one matrix factorization and m back-solves at each iteration. Different factorization subroutinescan be chosen in order to take advantage of the structureof the problem. Numerical results are presented for a largecollection of linear complementarity problems arising in thesimulation of multibody systems with contacts and frictionand in equilibrium problems for energy markets.

Cosmin PetraUniversity of Maryland BaltimoreDepartment of Math & Statistiscpetra1@umbc.edu

MS48

Complementarity Problems over Symmetric Cones

We present a class of interior point methods for solving lin-ear complementarity problems over symmetric cones. Themethods use adaptive long steps to produce iterates in awide neighborhood of the central path. We prove poly-nomial complexity , and we give sufficient conditions un-der which the duality gap converges superlinearly to zero.We also describe two large scale practical applications in-volving direct products of second order cones and cones ofpositive semidefinite matrices.

Florian A. PotraUniversity of Maryland Baltimore CountyDepartment of Mathematics and Statisticspotra@math.umbc.edu

MS48

Homogeneous Algorithms for Monotone ConicComplementarity Problems

For monotone conic complementarity problems, a homoge-neous model has been proposed for which a bounded pathhaving a trivial starting point exists: if the problem is solv-able then it gives us a solution, if the problem is stronglyinfeasible, then it gives us a certificate proving infeasibil-ity. We describe a class of algorithms for tracing the pathabove. For linear problems, polynomial iteration complex-ity bounds of the algorithms are derived.

Akiko YoshiseUniversity of Tsukubaraduate School of Systems and Information Engineeringyoshise@sk.tsukuba.ac.jp

MS49

The DAKOTA Toolkit for Parallel Optimizationand Uncerainty Analysis

DAKOTA is a Sandia National Laboratories toolkit foroptimization, uncertainty quantification, and sensitivityanalysis with large-scale computational models. Throughstrategies, its algorithms may be combined with each otherand/or with global or local surrogate models. I will sur-vey the DAKOTA framework, including available methods,modes of parallelism, and design abstractions. Examplesincluding surrogate-based optimization, optimization un-der uncertainty, and efficient global reliability assessmentwill illustrate benefits of hybrid methods. DAKOTA isfreely available from http://www.cs.sandia.gov/DAKOTA.

Brian M. AdamsSandia National LaboratoriesOptimization/Uncertainty Estimationbriadam@sandia.gov

MS49

Computing Architectures for Design Space Explo-ration Methods

Over the last few years great progress has been made indesign space exploration methods. These methods havein common that they generally address problems involvinglong running computer codes. They can try to providean understanding of the relationship between inputs andoutputs, perform single- or multi-objective optimizations,or design under uncertainty. To successfully apply thesemethods appropriate architectures are needed. This talkwill provide an overview of such architectures.

Joerg M. GablonskyMathematics & Engineering AnalysisPhantom Works - The Boeing CompanyJoerg.M.Gablonsky@boeing.com

MS49

The Acro/COLIN Framework: Developing Flex-ible Optimization Interfaces for Parallel, Hybrid,and Dynamically-Configured Algorithms

Most optimization programming interfaces force both theapplication and the algorithm to use common data typesand common optimization problem models (e.g. MINLP).In contrast, the Acro/COLIN framework decouples datatype dependence between application and algorithm, sup-ports extensible problem representations, and facilitatesthe rapid construction of hybrid algorithms. We willpresent an overview of the core capabilities of Acro/COLINand its application to the development of Agent-basedOptimization, a hybrid asynchronous optimization meta-algorithm.

William E. HartSandia National LaboratoriesDiscrete Mathematics and Complex Systemswehart@sandia.gov

John D. SiirolaSandia National LaboratoriesExploratory Simulation Technologiesjdsiiro@sandia.gov

MS49

Manifold-Based Learning and Search Techniquesfor Semi-Interactive Global Optimization

Recent experimental evidence indicates high-quality solu-tions to global optimization problems can reside on low-dimensional non-linear manifolds. The existence of suchmanifolds has key implications for the design of bothautomated and semi-interactive global optimization algo-rithms. We discuss techniques for identifying such mani-folds on standard benchmark problems, surrogate searchalgorithms based on the resulting manifolds, and semi-interactive search driven by human manifold analysis.

Jean-Paul WatsonSandia National LaboratoriesDiscrete Math and Complex Systemsjwatson@sandia.gov

MS50

An Optimization Approach for Generating Se-

112 OP08 Abstracts

quences of Radiotherapy Treatment Plans

A method for generating sequences of intensity-modulatedradiotherapy treatment plans is presented. The goal is tosupport the physician in finding a sound trade-off betweenplan quality and treatment complexity. The method is in-fluenced by column generation approaches and alternatesbetween solving a nonlinear problem and a restricted con-vex problem. Similarities between the proposed methodand the conjugate-gradient method for convex quadraticprogramming problems are discussed. Results on clinicalcases are presented as well.

Fredrik CarlssonRoyal Institute of Technology, Swedenfcar@kth.se

MS50

Blending Mathematics, Computation and Physicsinto a Treatment Planning System

Optimally designing radiotherapy treatments is a popu-lar and meaningful area of research, but the communitylacks a complete open-source treatment system that canaccommodate head-to-head comparisons of varying tech-niques. We will discuss the design and implementation ofa research oriented treatment design system that beginswith a patient’s geometry and prescription and ends witha treatment tailored to the treatment paradigm. To facil-itate broad testing of individual steps within the process,the system is built in modules that can be substituted withcompeting techniques.

Allen HolderDepartment of MathmaticsTrinity Universityaholder@trinity.edu

Arthur HannaSt. Mary’s University - TexasDepartment of Computer Scienceahanna@stmarytx.edu

Paul UhligSt. Mary’s University - TexasDepartment of Mathematicsmathpaul@stmarytx.edu

MS50

Large-Scale Optimization Strageties for OptimalCancer Treatment Design

Treatment planning for radiation therapy is inherentlycomplex due to the number of input parameters involved.The complexity is amplified by the uncertainty of targetshapes due to organ motion, by dose estimation, by avail-ability of biological information, and by competing multi-ple clinical objectives within the planning procedure. Inthis talk, we describe some of our experience in cancertreatment design related to these issues. Various optimiza-tion methods will be contrasted, and computational chal-lenges will be discussed. This work is joint with medicalresearchers from Washington University St. Louis.

Eva K. LeeGeorgia Inst of TechnologySch of Ind & Systems Engevakylee@isye.gatech.edu

MS50

Optimization of Image Guided Radiation Therapy

Intensity Modulated Radiation Therapy (IMRT) treat-ments are typically delivered in daily fractions rather thana single session. Recent developments in Image Guided Ra-diation Therapy (IGRT) are promising to provide dynamicinformation about the state of the tumor. This presenta-tion discusses optimization models that update the planafter every fraction and achieve the best IMRT design forboth fraction and overall treatment with the aim of cap-turing the changes in tumor position and the shape.

Ronald L. Rardin, Seda GumruksuUniversity of Arkansasrrardin@uark.edu, sgmr@uark.edu

Mark LangerIndiana University School of MedecineIndianapolis, INmlanger@iupui.edu

MS51

Provably Optimal Solutions to Geometric VisionProblems

In the past, the main methods for solving problems inMultiview Vision Geometry have been iterative techniques,which may suffer from falling into local minima, and trou-ble with convergence. Recent research has turned to find-ing guaranteed globally optimal solutions to such problems.Techniques include quasi-convex optimization, Second Or-der Cone Programming, Branch-and-bound techniques andfractional programming, solving many of the common vi-sion geometry problems. In this talk, we address problemssuch as essential-matrix estimation, many-view triangula-tion and motion of a vehicle with rigidly placed cameras.We provide optimal solutions, (in L2 or L-infinity norm)where no such solution existed previously (as of 2007).

Richard I. HartleyThe Australian National UniversityCanberra, AustraliaRichard.Hartley@anu.edu.au

Fredrik KahlUniversity of LundSwedenfredrik@maths.lth.se

MS51

Invariance Properties of Newton-Type Methods onReductive Homogeneous Spaces

Newton-type methods on differentiable manifolds becamerecently very popular, from a theoretical and from an ap-plication point of view as well. We discuss invariance prop-erties for these methods on a very rich class of smooth man-ifolds, namely reductive homogeneous spaces. The invari-ance properties we present are a generalisation of the wellknown affine invariance properties of Newton’s method onEuclidean spaces. A few examples from signal processingand computer vision are given to explain the details.

Knut HueperNICTA Canberra Research LaboratoryCanberra, Australiaknut.hueper@nicta.com.au

OP08 Abstracts 113

Jochen TrumpfThe Australian National Univ.and National ICT Australia Ltdjochen.trumpf@anu.edu.au

MS51

Local Convergence Properties of Conjugate Gradi-ent Methods on Manifolds

The local convergence properties of conjugate gradientmethods on smooth manifolds are usually harder to anal-yse than their counterpart on vector spaces. We presentrecent results in this direction, exemplified by implemen-tations of the CG method in the area of signal processing,namely simultaneous diagonalisation of several covariancematrices.

Martin KleinsteuberMath. Institute, University WuerzburgGermanykleinsteuber@mathematik.uni-wuerzburg.de

Knut HueperNational ICT Australia LtdKnut.Hueper@nicta.com.au

MS51

The Basis Partition of the Space of Linear Pro-grams

We consider the space of all linear programs with n non-negative variables and m equality constraints. Each linearprogram (LP) is associated with a basis (a basis is a subsetof indices 1,2,,n), in the sense that the limit of the centralpath of the LP, which is an optimal solution of the LP, cor-responds to a unique basis. There are only a finite numberof bases. Thus, the space of linear programs (SLP) can bepartitioned into a finite number of sets S1, S2, , Sk, eachset containing all LPs which are associated with a commonbasis, (so called the basis partition). If this partition of theSLP can be explicitly characterized, then we can solve anyset of (infinitely many) linear programs, e.g. a parametricLP, in the closed form. A novel tool for characterizing thispartition of the SLP is presented as follows. Relating tothe central path, there exists a universal ordinary differen-tial equation M’=h(M) defined on projection matrices M.For any LP, one can define a projection matrix, startingfrom which the solution of M’=h(M) converges to a limitprojection matrix which can determine the optimal basis ofthe LP. This establishes a corresponding partition on thespace of projection matrices, denoted by G. G is the well-known Grassmann manifold. With the help of the vectorfield h(M) on the Grassmann manifold G, it is promisingto discover full characterization of the partition of the SLP.We will present some properties related to the SLP foundso far. Full structure of the basis partition of SLP is stillawaiting an exploration.

Gongyun ZhaoDepartment of MathematicsNational University of Singaporematzgy@nus.edu.sg

MS52

Multi-Secant Equations, Approximate InvariantSubspaces and Multigrid Optimization

New approximate secant equations are shown to result from

the knowledge of (problem dependent) invariant subspaceinformation, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. It is alsoshown that this type of information may often be extractedfrom the multigrid structure of discretized infinite dimen-sional problems. A new limited-memory BFGS using ap-proximate secant equations is then derived and its encour-aging behaviour illustrated on a small collection of multi-level optimization examples. The smoothing properties ofthis algorithm are considered next, and automatic genera-tion of approximate eigenvalue information demonstrated.The use of this information for improving algorithmic per-formance is finally investigated on the same multilevel ex-amples.

Serge GrattonCNESserge.gratton@cnes.fr

Philippe L. TointThe University of NamurDepartment of Mathematicsphilippe.toint@fundp.ac.be

MS52

Control Constrained Optimal Control of Time-Dependent Convection Diffusion by the Discon-tinuous Galerkin Method dg(1) in Time andSDFE(streamline Diffusion Finite Element) Dis-cretization in Space

We consider optimal control of (time–dependent) convec-tion diffusion equations. To discretize the optimal controlproblem we use the variational discrete concept proposed in[?]. In this approach the cost functional is approximated bya sequence of functionals which are obtained by discretizingthe state equation with the help of a dg(1) discretizationin time and SDFE discretization in space. The controlvariable is not discretized. Error bounds for control andstate are obtained both in two and three space dimensions.The numerical implementation of a semi–smooth Newtonmethod for the variational–discretized problem is describedin detail. Finally, we present numerical experiments whichconfirm our analytical findings.

Bulent KarasozenMiddle East Technical UniversityTurkeybulent@metu.edu.tr

Michael HinzeDepartment of MathematicsUniversity of Hamburgmichael.hinze@uni-hamburg.de

Morton VierlingUniversity of Hamburgvierling@math.uni-hamburg.de

Songul Kaya MerdanMiddle East Technical University Ankarasmerdan@metu.edu.tr

Hamdullah YucelInstitute of Applied MathematicsMiddle East Technical Universitye132741@metu.edu.tr

114 OP08 Abstracts

MS52

A Multilevel Adaptive Cubic Overestimation Tech-nique

C. Cartis, N. Gould and Ph. Toint have recently proposeda new algorithm for unconstrained nonlinear optimizationwhere a cubic model of the objective function is contructedat each iteration. The model cubic term is then updatedusing a ”trust-region radius update”-like process. In thistalk, we present the application of the multilevel philosophyto this method, some numerical results and possible futurediscussions.

Dimitri TomanosUniversity of NamurBelgiumdimitri.tomanos@fundp.ac.be

MS52

Multilevel Trust-Region Methods for Bound-Constrained Optimization

We present a globally convergent multilevel trust-regionmethod for large-scale bound-constrained optimizationproblems. The method relies on a coarse-to-fine hierar-chy of objective functions. This setting arises, e.g., wheninfinite-dimensional optimization problems are discretizedat different scales. The algorithm uses the coarser versionsto generate steps in a way similar to the full approximationmultigrid scheme. The bound constraints are handled byan active-set strategy and by a natural feasibility conditionon lower levels.

Boris von LoeschTechnical University of Munichvloesch@ma.tum.de

Michael UlbrichTechnical University of MunichChair of Mathematical Optimizationmulbrich@ma.tum.de

MS53

Uncertainty Quantification in PDE-Based InverseProblems

The structure of many PDE-based inverse problems per-mits very fast solution and very cheap approximation ofthe Hessian of the misfit via inexact Newton-CG meth-ods (where ”fast” and ”cheap” mean at a cost of a con-stant number of forward solutions). The connection forthe linear/Gaussian case between minimization of regular-ized least squares misfit functions and full Bayesian inversesolution underscores the role of fast optimization methodsin uncertainty quantification. We discuss some preliminaryideas on how such such structure-exploiting techniques canbe brought to bear on Bayesian analysis of nonlinear/non-Gaussian inverse problems. Examples from state estima-tion for advective-diffusive transport and parameter esti-mation for wave propagation are used to illustrate the mainideas.

Omar GhattasUniversity of Texas at Austinomar@ices.utexas.edu

MS53

Optimal Control of the Thermistor Problem

The presented talk deals with the optimal control of thethermistor problem that models the conductive heat trans-fer in a conductor produced by an electric current. Thisleads to a quasi-linear system of partial differential equa-tions (PDEs) with mixed boundary conditions. A possibleapplication for this coupled system of PDEs is the hard-ening of steel workpieces via the Joule effect. However,for practical applications, it is necessary to obey pointwisestate constraints that guarantee that the melting temper-ature is not exceeded. This kind of constraints is knownto be numerically and theoretically challenging to handlesince continuity of the state is required and the associatedmultipliers are only measures in general. Using maximumparabolic and elliptic regularity results, we establish conti-nuity of the state and existence for solutions of the adjointequation which leads to first-order necessary conditions.The problem is solved numerically by means of a Moreau-Yosida type regularizaton of the state constraints. Thefeasibility of this approach is afterwards demonstrated bythe example of hardening a gear rack.

Dietmar HoembergWeierstrass Institute for Applied Analysis and Stochasticshoemberg@wias-berlin.de

Christian MeyerWIAS, Berlinmeyer@wias-berlin.de

Joachim RehbergWeierstrass Institute for Applied Analysis and Stochasticsrehberg@wias-berlin.de

Wolfgang RingInstitut fuer MathematikUniversitaet Grazwolfgang.ring@kfunigraz.ac.at

MS53

On an ODE-PDE Constrained Optimal ControlProblem with Applications to Hypersonic FlightUnder Heat Load Constraints

During ascent and reentry of a hypersonic space vehicleinto the atmosphere of any heavenly body, the space vehi-cle is subjected to extreme aerothermic loads. Therefore anefficient, sophisticated and lightweight thermal protectionsystem is determinative for the success of the entire mis-sion. For a deeper understanding of the conductive, con-vective and radiative heating effects through a thermal pro-tection system, a mathematical model is investigated whichis given by an optimal control problem subject to not onlythe usual dynamic equations of motion and suitable controland state variable inequality constraints for the ODE partof the problem, but also subject to an instationary quasi-linear heat equation with nonlinear boundary conditionsand a state constraint, forming the PDE part of the prob-lem. By this model the temperature of the heat shield canbe limited in certain critical regions. The resulting ODE-PDE constrained optimal control problem is, because of itscomplexity, solved by the approach First discretize, thenoptimize. The discretization scheme used is a second-orderfinite-volume scheme in space for the semi-discretization ofthe quasi-linear parabolic partial differential equation in itsspace variables. This yields a large scale nonlinear ODEconstrained optimal control problem with multiple state

OP08 Abstracts 115

and/or control variable inequality constraints, in particu-lar for the limitation of the heat load. This problem isalso solved by the approach First discretize, then optimizeand ends in a large scale non-linear programming prob-lem. Numerical results are presented. They show, that theaerothermic load and the fuel loss can be considerably re-duced by optimization. Some theoretical light on this prob-lem is given by the investigation of an academic problem ofan equivalent structure, which is based on the well-knownclassical harmonic oscillator problem, which has illustratedthe development of the maximum principle and thereforeis called the hypersonic oscillator.

Kurt ChudejUniversity of Bayreuthkurt.chudej@uni-bayreuth.de

Hans Josef PeschUniversity of Bayreuth, GermanyChair of Mathematics in Engineering Scienceshans-josef.pesch@uni-bayreuth.de

Markus WaechterTechnical University Munichwaechter@lfm.mw.tu-muenchen.de

MS53

Optimization Methods for Some Problems in Fi-nance

In this talk we consider several aspects of optimizationproblems in finance from a numerical point of view. In par-ticular we investigate the use of optimization methods forcalibration problems and their relation to nonlinear leastsquares problems. These problems are formulated as PDE-constrained optimization problems as well as optimizationproblems with SDE-constraints. We discuss the numericalsolution and the use of adjoint variables in this context.We apply these techniques to some calibration problemsfor standard and nonstandard models for the pricing ofoptions.

Ekkehard W. SachsUniversity of TrierVirginia Techsachs@uni-trier.de

MS54

Obtaining Optimal k-Cardinality Trees Fast

Given an undirected graph G = (V,E) with edge weightsand a positive integer number k, the k-Cardinality Treeproblem is to find a subtree T of G with exactly k edgesand the minimum possible weight. Many algorithms havebeen proposed to solve this NP-hard problem, resultingin mainly heuristic and metaheuristic approaches. In thispaper we present an exact ILP-based algorithm using di-rected cuts. We mathematically compare the strength ofour formulation to the previously known ILP formulationsof this problem, and give an extensive study on the al-gorithm’s practical performance compared to the state-of-the-art metaheuristics. In contrast to the widespread as-sumption that such a problem cannot be efficiently tackledby exact algorithms for medium and large graphs (between200 and 5000 nodes), our results show that our algorithmnot only has the advantage of proving the optimality of thecomputed solution, but also often outperforms the meta-

heuristic approaches in terms of running time.

Markus Chimani, Maria KandybaDortmund UniversityGermanymarkus.chimani@cs.uni-dortmund.de,maria.kandyba@cs.uni-dortmund.de

Ivana LjubicUniversity of Viennaivana.ljubic@univie.ac.at

Petra MutzelDortmund UniversityGermanypetra.mutzel@cs.uni-dortmund.de

MS54

Strong Formulations for 2-Node-Connected SteinerNetwork Problems

We consider a survivable network design problem knownas the 2-Node-Connected Steiner Network Problem(2NCON): we are given a weighted undirected graph witha node partition into two sets of customer nodes and oneset of Steiner nodes. We ask for the minimum weight con-nected subgraph containing all customer nodes, in whichthe nodes of the second customer set are nodewise 2-connected. This problem class has received lively atten-tion in the past, especially with regard to exact ILP for-mulations and their polyhedral properties. In this talk,we present a transformation of this problem into a relatedproblem considering directed graphs and use this to estab-lish two novel ILP formulations to solve 2NCON, based onmulti-commodity flow and on directed cuts, respectively.We prove the advantages of our formulations and com-pare both approaches theoretically as well as experimen-tally. Thereby we solve instances with up to 1600 nodes toprovable optimality.

Markus Chimani, Maria KandybaDortmund UniversityGermanymarkus.chimani@cs.uni-dortmund.de,maria.kandyba@cs.uni-dortmund.de

Ivana LjubicUniversity of Viennaivana.ljubic@univie.ac.at

Petra MutzelDortmund UniversityGermanypetra.mutzel@cs.uni-dortmund.de

MS54

Multi-Period Traffic Routing in Satellite Networks

We introduce a traffic routing problem over an extendedplanning horizon that appears in geosynchronous satellitenetworks. Unlike terrestrial networks, routing on a satel-lite network is not transparent to the customers. As aresult, a route change is associated with significant mone-tary penalties that are usually in the form of discounts (upto 40%) offered by the satellite provider to the customerthat is affected. The notion of these re-routing penaltiesrequires the network planners to look at routing decisionsover multiple time periods and introduces novel challenges

116 OP08 Abstracts

that have not been considered previously in the literature.We develop a branch-and-price-and-cut procedure to solveboth the deterministic and stochastic version of this prob-lem and describe an algorithm for the associated pricingproblem. Computational work will be discussed.

S. RaghavanThe Robert H. Smith School of BusinessUniversity of Maryland, USAraghavan@umd.edu

Ioannis GamvrosILOGgamvros@gmail.com

MS54

Approaches for a Single-Source Network DesignProblem

Let us consider a network G=(N,A) where a node is asource and some others are destinations. Each arc is re-lated to a set of cables, and these cables are sorted intypes according to capacities. A cable type can only beused for an arc if all the precedence types have also beenused for this arc. The problem is to decide the cables toinstall in each arc to guarantee serving the demands of alldestinations from the source at minimum cost. We an-alyze and compare different flow formulations and theirflow-projected formulations. We also discuss the variantwhere the solution must be a tree.

Juan Jose Salazar-GonzalezFaculty of MathematicsUniversity of La Laguna, Spainjjsalaza@ull.es

Ivana LjubicUniversity of Viennaivana.ljubic@univie.ac.at

Inmaculada Rodriguez MartinUniversity of La Laguna, Spainirguez@ull.es

Peter PutzUniversity of Vienna, Austriap.putz@univie.ac.at

MS55

New Worst Cases for Polynomial Optimization ViaGroup-Invariant SDPs

This talk presents the first unrestricted family of poly-nomials which are non-negative but not sums-of squares.The presented construction demonstrates the use of group-representation theory in semi-definite programs (SDP) re-sulting from polynomial optimization problems. Surprisingat first sight only, not every non-negative (PSD) polyno-mial is a sum of squares (SOS) of other polynomials. Therelation between PSD and SOS polynomials is far from be-ing only a historically challenging topic; the hardness ofpolynomial optimization actually comes in via the differ-ence between the two. But although there are (provably)many polynomials which are PSD but not SOS, few arecurrently known. The talk presents a family of PSD poly-nomials which are not SOS, encompassing all previouslyknown examples. Moreover, the construction presented inthe talk may serve as an explicit example of the use of

group-representation theory in order to reduce the size ofSDPs.

Hartwig BosseJ.W. Goethe-UniversitatFrankfurt am Main, Germanybosse@math.uni-frankfurt.de

MS55

Properties of Symmetry Reduction for Semidefi-nite Programs

In this talk we consider the mathematical properties ofcertain symmetry reductions for semidefinite programs(SDP’s), where the SDP data matrices lie in some matrixalgebra. We generalize the so-called regular *-reductiontechnique to this setting, and provide some examples toillustrate the procedure. We also compare various otherreduction techniques from the recent literature to the reg-ular *-reduction.

Cristian DobreTilburg UniversityTilburg, The NetherlandsC.Dobre@uvt.nl

Etienne De KlerkTilburg UniversityE.deKlerk@uvt.nl

MS55

Exploiting Group Symmetry in SDP Relaxation ofthe QAP

The Quadratic Assignment Problem (QAP) contains thetraveling salesman problem as a special case and even smallinstances are notoriously difficult to solve in practice. Inthis talk we consider semidefinite programming relaxationsof the QAP, and show how to exploit algebraic symmetry ofthe data matrices when present, in order to greatly reducethe size of the relaxations. This approach has allowed usto compute the best known bounds for several instancesfrom QAPLIB.

Renata Sotirov, Etienne De KlerkTilburg Universityr.sotirov@uvt.nl, E.deKlerk@uvt.nl

MS55

Lower Bounds for Measurable Chromatic Numbers

The chromatic number of n-dimensional Euclidean space isthe minimum number of colors needed to color all points sothat no two at unit distance get the same color. One speaksof the measurable chromatic number when the color classesare measurable. Finding the (measurable) chromatic num-ber of the plane is a famous open problem. Using a gen-eralization of Lovasz theta-function and basic tools fromfunctional analysis we obtain new lower bounds in severaldimensions.

Christine BachocUniv. Bordeauxchristine.bachoc@math.u-bordeaux1.fr

Gabriele NebeRWTH Aachennebe@math.rwth-aachen.de

OP08 Abstracts 117

Fernando Mario de Oliveira Filho, Frank VallentinCentrum voor Wiskunde en InformaticaAmsterdam, The Netherlandsf.m.de.oliveira.filho@cwi.nl, F.Vallentin@cwi.nl

MS56

YAS: An Open-source C++ Platform for RapidIPM Development with SMP

We present an object-oriented open-source platform YAS(Yet Another Solver) for rapid porting, prototyping anddevelopment of interior-point method algorithms in C++,targeted for SMP architecture – symmetric multiprocess-ing with multiple CPUs sharing a common memory. YASis particularly designed to allow easy extensions of IPM be-yond the symmetric cone programming, e.g., p-norm cones,and the underlying direct linear algebra solvers, e.g., PCG.To achieve near-peak CPU performance, YAS provides atransparent interface between pre-tuned BLAS libraries,such as Intel MKL, AMD ACML and ATLAS. To takethe advantage of some common features of IPM and thelinear algebra, special objects are introduced. Currentlywithin the platform, basic primal short-step, long-step,predictor-corrector, and Nesterovs asymmetric primal-dualpredictor-corrector methods are implemented. YAS pro-vides SeDuMi-like data input interface for MATLAB andOctave, with the capability of building standalone appli-cations. In addition, for SDP YAS allows specification ofmatrix-pencils in their native form.

Voicu ChisMcMaster University, Canadachisv@math.mcmaster.ca

Yuriy ZinchenkoMcMaster Universityzinchenko@mcmaster.ca

Tamas TerlakyDept. of Computing and SoftwareMcMaster Universityterlaky@mcmaster.ca

MS56

Criss-Cross Algorithm for General Linear Compla-mentarity Problem

Fukuda and Terlaky (1992) worked out some connectionsbetween Linear Complementarity Problems (LCP) andOriented Matroids. In their paper they introduced dualproblem and proved a Farkas-type alternative theorem. Upto our best knowledge, this is the first paper in which alter-native theorem for LCP has been stated and proved. (Theirresult was called duality theorem by them; however we feelthat the alternative theorem for LCP is better name fortheir result.) Den Hertog, Roos and Terlaky (1993) provedthat the minimal index criss-cross algorithm for LinearComplementarity Problem (LCP) is finite if the matrix ofthe problem is sufficient. Fukuda, Namiki and Tamura(1998) applying the concept of EP-theorem introduced byCameron and Edmonds (1990) for the LCP problems givenby rational data, modified the minimal index criss-crossalgorithm in such a way that they either solve the primalLCP, or the dual LCP or give a polynomial size certifi-cate that the matrix is not sufficient. In this talk we showthat the minimal index rule can be replaced by the last-in-first-out (LIFO) and most-often-selected-variable (MOSV)rules and still to prove the finiteness of the criss-cross al-gorithm. Similar modifications that Fukuda, Namiki and

Tamura used in their paper, enables us to generalize ourfinite variants of the criss-cross method for general LCPproblems and to solve those in the sense of the correspond-ing EP-theorem. Technically, we need to assign label toeach variable and update the vector formed from the la-bels according to the pivot rule. The vector formed fromthe labels play an important role in proving the finiteness ofthe criss-cross algorithm. Further generalization of the be-haviour of these pivot rules (minimal index, LIFO, MOSV)led to the definition of the class of s-monotone pivot rulesand the related results.

Tibor IllesManagement Science DepartmentUniversity of Strathclydetibor.illes@strath.ac.uk

Zsolt CsizmadiaOperations Research DepartmentEotvos Lorand Universityzsolt.csizmadia@gmail.com

MS56

Interior Point Algorithms for General Linear Com-plementarity Problems

The LCPs are usually NP-hard problems. The largest ma-trix class where the interior point algorithms (IPM) arepolynomial is the class of P∗(κ)-matrices. We modify theIPMs such that either solve LCPs or give a certificate thatproves the matrix does not belong into the class of P∗(κ)-matrices, or show the unsolvability of the LCP. The mod-ified algorithm is still polynomial, but does not give in allcases a solution for solvable LCPs.

Tibor IllesManagement Science DepartmentUniversity of Strathclydetibor.illes@strath.ac.uk

Marianna NagyDepartment of Operations ResearchEotvos Lorand Universitynmariann@cs.elte.hu

Tamas TerlakyDept. of Computing and SoftwareMcMaster Universityterlaky@mcmaster.ca

MS56

Improved Approximation Bound for QuadraticOptimization Problems with Orthogonality Con-straints

In this talk we consider approximation algorithms fora class of quadratic optimization problems that containorthogonality constraints, i.e. constraints of the formXTX = I, where X ∈ Rm×n is the optimization variable.Such class of problems, which we denote by (QP-OC), isquite general and captures several well-studied problems inthe literature as special cases. In a recent work, Nemirovski[Math. Prog. 109:283-317, 2007] gave the first non-trivial

approximation algorithm for (QP-OC). His algorithm isbased on semidefinite programming and has an approxima-tion guarantee of O((m+n)1/3). We improve upon this re-sult by providing the first logarithmic approximation guar-

118 OP08 Abstracts

antee for (QP-OC). Specifically, we show that (QP-OC)can be approximated to within a factor of O(ln maxm,n).The main technical tool used in the analysis is a concen-tration inequality for the spectral norm of a sum of cer-tain random matrices, which we develop using tools fromfunctional analysis. Such inequality also has ramificationsin the design of so-called safe tractable approximations ofchance constrained optimization problems. In particular,we use it to improve a recent result of Ben-Tal and Ne-mirovski [Manuscript, 2007] on certain chance constrainedlinear matrix inequality systems.Anthony Man-Cho SoThe Chinese University of Hong Kong, Hong Kongmanchoso@se.cuhk.edu.hk

MS57

Approximate Solutions in Vector Optimization

In vector optimization there are different kinds of approxi-mate solutions. Thus, in the literature we can find Loridan-Kutateladze approximate solutions [2,3], Tanaka approxi-mate solutions [4] and Bonnel approximate solutions [1].It will be shown that in general these concepts are notequivalent. However, under some suitable hypothesis, wewill present some connections between the asymptotical be-haviour of sequences of such approximate solutions. Ref-erences [1] S.Bolintineanu (H.Bonnel), Vector variationalprinciples; ”epsilon-efficiency and scalar stationarity,” J.Convex Anal., Vol. 8, pp. 71-85, 2001. [2] S.S.Kutateladze,Convex epsilon-programming,” Sov.Math.Dokl., Vol. 20,pp. 391-393, 1979. [3] P. Loridan, ”epsilon-Solutions invector minimization problems,” J. Optim Theory Appl.,Vol. 43, pp. 265-276, 1984. [4] T.Tanaka, A new ap-proach to approximation of solutions in vector optimiza-tion problems,” in M. Fushini, K. Tone (eds.) Proceedingsof APORS 1994, pp. 497-504, World Scientific, Singapore,1995.

Henri BonnelUniversite de la Nouvelle-Caledoniebonnel@univ-nc.nc

MS57

A Set-Valued Approach to Duality in Vector Opti-mization and Applications.

We show that the theory of Multiple Objective Program-ming (MOP) can be described quite analogously to SingleObjective Programming, when it is considered in a set-valued framework. This approach leads to a new dualitytheory for MOP. For the linear case we present an inter-pretation of the duality theory which is closely related tothe classical idea of ”duality of polytopes”. As an appli-cation we present an algorithm for solving linear multipleobjective problems.

Andreas Loehne, Frank HeydeInstitute of MathematicsUniversity of Halle-Wittenbergandreas.loehne@mathematik.uni-halle.de,frank.heyde@mathematik.uni-halle.de

MS57

Multicriteria Optimization in Medical Engineering

Multicriteria optimization problems often arise in medicalengineering research. We investigate two nonlinear prob-lems from magnetic resonance imaging (MRI) and parti-cle therapy. In case of MRI, homogeneity of the B1-fieldand patient exposure were optimized simultanously with avery large number of constraints, whereas for particle ther-apy we had several highly nonlinear criteria on ion optics.These problems were solved with a constraint method. Weshow their special challenges and present numerical results.

Eva SchneiderSiemens AG, Erlangeneva.i.schneider@arcor.de

MS57

Lipschitz Properties of the Scalarization Functionand Applications.

The scalarization functions were used in vector optimiza-tion for a long period. Similar functions were introducedand used in economics under the name of shortage functionor in mathematical finance under the name of (convex orcoherent) measures of risk. The main aim of this talk is tostudy Lipschitz continuity properties of such functions andto give some applications for deriving necessary optimal-ity conditions for vector optimization problems using theMordukhovich subdifferential.

Christiane TammerFaculty of Sciences III, Institute of MathematicsUniversity of Halle-Wittenbergchristiane.tammer@mathematik.uni-halle.de

Constantin ZalinescuUniversity Al.I.Cuza IasiFaculty of Mathematics, Iasi, Romaniazalinesc@uaic.ro

MS58

Large Scale Cone Complementarity Problems forRigid Body Dynamics with Contact and Friction

We present a class of iterative methods to solve the conecomplementarity subproblems that appear in the simula-tion of nonsmooth rigid body dynamics with contact andfriction. We prove that the method is globally convergent.Through numerical experiments, we demonstrate that themethod scales linearly with with an increasing size of theproblem up to millions of vatiables and show that it is verycompetitive for the simulation of granular flow dynamics.

Mihai AnitescuArgonne National LaboratoryMathematics and Computer Science Divisionanitescu@mcs.anl.gov

MS58

Adjoint Sensitivity Analysis of Hybrid Dis-

OP08 Abstracts 119

crete/Continuous Systems

We present a general framework for adjoint sensitivity anal-ysis of a broad class of hybrid discrete/continuous systemsdescribed, in their continuous regime, by differential alge-braic equation (DAE) systems. This works extend existingresults on forward sensitivity analysis of such systems by:(a) considering Hessenberg index-2 DAEs, besides ODEand index-1 DAEs’ (b) including the analysis of systemswith “memory”, that is systems whose dynamics dependon the states (and possibly the state derivatives) at the lasttransition time, where a discrete event occurred; and (c)providing the analysis for adjoint sensitivity analysis, in-cluding the derivation of the appropriate adjoint systems,the equations for the transfer of adjoint variables at transi-tion points, and the resulting sensitivity of the quantity ofinterest. We provide several illustrative examples, includ-ing a more complex model from structural dynamics whichuses a hybrid plasticity constitutive material law.

Radu SerbanLawrence Livermore National LaboratoryCenter for Applied Scientific Computingserban1@llnl.gov

MS58

An Algorithm for Finding Equilibria of StochasticGames

The talk discusses a hybrid algorithm for finding Nash equi-libria of stochastic games. The algorithm combines pro-jected dynamical systems with an interior point methodfor solving MPEC’s. Global convergence results and nu-merical results will be discussed.

David ShannoRutgers UniversityNew Brunswick, NJ 08903shannod@comcast.net

MS58

Uniqueness of Solutions for Differential VariationalInequalities

Differential variational inequalities are differential equa-tions where the right-hand side is determined (in part) bythe solutions of variational inequalities. Here we considerlinear differential equations with a variational inequality ofthe form

dx

dt(t) = Ax+B u(t), x(t0) = x0,

u(t) ∈ K for all t,

0 ≤ (w − u(t))T (Cx(t) + g(t)) for all t.

It has recently been shown that solutions exist if CB is pos-itive definite, but uniqueness has only be shown in generalif CB is also symmetric. Examples of non-uniqueness aredemonstrated, and examples of non-symmetric CB givinguniqueness are shown. Open questions regarding unique-ness are mentioned along with applications of this result.

David E. StewartUniversity of IowaDepartment of Mathematics

dstewart@math.uiowa.edu

MS59

Recent Numerical Experiences With Large ScaleGroundwater Management

Groundwater management models couple complex ground-water simulation models with optimization techniques.Groundwater simulation models with large spatial domainsand long time horizons can present special challenges forsuccessful optimization, even when groundwater flow is theonly state under consideration. In this talk, a number ofcase studies are reviewed highlighting numerical and algo-rithmic issues that arise in solving large scale groundwatermanagement problems.

David AhlfeldUniversity of Massachusetts AmherstDepartment of Civil and Environmental Engineeringahlfeld@ecs.umass.edu

MS59

Derivative-Free Benchmarking Problems from Wa-ter Resources Management

We present a set of problems from hydrology used to com-pare derivative-free optimization algorithms. We describethe applications, various simulation-based problem formu-lations, and show comparison results obtained with a va-riety of methods including implicit filtering, several im-plementations of pattern search, a genetic algorithm, DI-RECT, and surrogate model approaches. Finally, we pro-vide information about downloading the test problems forthe application, testing, and comparison of other applica-ble optimization algorithms.

Kathleen FowlerClarkson UniversityDepartment of Mathematicskfowler@clarkson.edu

MS59

A Modified Simulated Annealing Approach forSolving Constrained Optimal Groundwater

Determining an optimal pump and treat groundwater re-mediation design subject to constraints defined by maxi-mal concentrations of contamination requires finding thesolution to a linear optimization problem bounded by non-linear constraints. Because parameters defining the prop-erties of groundwater flow are uncertain, a multiscenarioapproach is taken to include the uncertainty in the modeldesign. When this is done, the objective function, as wellas the constraints, are nonlinear and finding a solution tothis optimization problem requires the use of an efficientalgorithm that avoids unnecessarily calling the flow andtransport numerical model. By combining features of asimulated annealing algorithm with a gradient method, asolution to this optimization problem is determined. Themethod that is presented in this talk is one that dynam-ically changes as the search algorithm moves through thefeasible region, thereby taking into consideration elementssuch as the approximate gradient of the objective function

120 OP08 Abstracts

and the proximity to the boundary of the feasible region.

Karen L. RicciardiUniversity of Massachusetts BostonKaren.Ricciardi@umb.edu

MS59

POD Calibration for Groundwater Models in ADH

We are solving inverse problems in groundwater modeling.Given values of hydraulic head at discrete locations, weseek to approximate values of hydraulic conductivity forthe entire field. We are using ADH, a finite element codedeveloped at the Coastal and Hydraulics Lab in Vicksburg,MS. When using ADH to model large, complex groundwa-ter behavior – for instance the entire state of Florida – ex-treme run-times prohibit the frequent function calls neededfor parameter estimation. Proper Orthogonal Decomposi-tion (POD) is a method to reduce the size of the problemto calibrate ADH, reducing the number of full functioncalls needed. We will introduce the problem, discuss PODand how it is used for steady-state problems, and demon-strate the accuracy of the POD solution compared to thefull ADH solution.

Corey WintonNorth Carolina State Universitycorey.winton@gmail.com

MS60

On Solving the Newton Equation System WithinInterior-Point Methods for Linear and Conic Opti-mization Problems.

The purpose of this talk is to review the methods em-ployed to solve the Newton equation system arising withininterior-point methods for linear and conic optimizationproblems. The focus will be on the methods employedin commercial software such as MOSEK. Finally, we willpresent computational statistics detailing where time isspent when solving the Newton equation system. More-over, we hope to comment on whether indirect methodssuch as conjugate-gradient-based methods could be moreefficient than direct methods for solving the Newton equa-tion system.

Erling D. AndersenMOSEK ApSCopenhagen, Denmarke.d.andersen@mosek.com

MS60

Large-Scale Eigenvalue Problems, Trust Regionsand Regularization

We consider large eigenvalue problems for matrices of theform

B =

(α gT

g H

)

where H is an n× n real symmetric matrix, g is an n× 1real vector, and α is a scalar. Such problems arise, forexample, in the context of methods for trust-region sub-problems and regularization. We describe the eigenvalue

problem, discuss its connection with the underlying op-timization problem, and compare matrix-free approachessuch as the Implicitly Restarted Lanczos and the Jacobi-Davidson Methods on large trust-region and regularizationproblems.

Marielba RojasTechnical University of Denmarkmr@imm.dtu.dk

MS60

Methods for Large-Scale Eigenvalue Problems inOptimization

We review computational methods for large-scale eigen-value problems and offer suggestions for some problems ofthis type arising in optimization.

Gerard SleijpenDepartment of MathematicsUtrecht Universitysleijpen@math.uu.nl

MS60

IDR(s): A New Family of Efficient Algorithms forLarge Nonsymmetric Linear Systems

We present a new family of limited-memory iterative meth-ods for solving nonsymmetric systems of linear equations.Our technique is a generalisation of the IDR algorithm ofSonneveld. We describe the methods and illustrate theirperformance on test problems from applications includinginterior point methods in optimisation. Our results showthat our technique frequently outperforms state-of-the-artKrylov methods such as Bi-CGSTAB and CGS.

Martin van GijzenNumerical Analysis GroupDelft University of Technologym.b.vangijzen@ewi.tudelft.nl

Peter SonneveldDelft University of Technologyp.sonneveld@tudelft.nl

MS61

Interior-Point Methods for Mixed-Integer Nonlin-ear Conic Programming

In this talk, we will present a unified framework for solvingproblems involving nonlinear functions, cone constraints,and discrete variables using an interior-point method. Wewill give particular consideration to warmstarts and infea-sibility identification and present numerical results.

Hande Y. BensonDrexel UniversityDepartment of Decision Sciencesbenson@drexel.edu

MS61

Global Convergence of a Primal-Dual Interior-

OP08 Abstracts 121

Point Method for Nonlinear Programming

Many recent convergence results obtained for primal-dualinterior-point methods for NLP use assumptions of theboundedness of generated iterates. In this talk we discusshow such assumptions can be replaced by new assumptionson the NLP problem and analyze convergence of the newmethod from any initial guess.

Igor GrivaGeorge Mason Universityigriva@gmu.edu

Hande BensonDepartment of Decision Sciences, LeBow College ofBusinessDrexel Universityhvb22@drexel.edu

David ShannoRUTCORRutgers Universityshanno@rutcor.rutgers.edu

Robert J. VanderbeiOperations Research and Financial EngineeringDepartmentPrinceton Universityrvdb@princeton.edu

MS61

Extinguishing Poisson’s Spot with Linear Program-ming

A leading design concept for NASA’s upcoming planet-finding space telescope involves placing an occulter 70,000km in front of a 4-m telescope. The purpose of the occulteris to block the bright starlight thereby enabling the tele-scope to take pictures of planets orbiting the blocked star.Unfortunately, diffraction effects prevent a simple circularocculter from providing a fully dark shadow—a speciallyshaped occulter is required. In this talk I will explain howthis shape-optimization problem can be solved with linearprogramming.

Robert J. VanderbeiOperations Research and Financial EngineeringDepartmentPrinceton Universityrvdb@princeton.edu

MS62

Multigrid Optimization Schemes for OptimizationProblems with Bilinear Structure

Bilinear control problems as distributed parameter esti-mation problems pose theoretical and computational chal-lenges that are open or have been only partially ad-dressed. We discuss and compare two multigrid-based so-lution strategies for bilinear optimization problems withbilinear structure. On the one hand, we use the experiencegathered with the one-shot multigrid solution to design acollective smoothing multigrid scheme (CSMG). This ap-

proach is quite robust and it provides typical multigridefficiency. However, its development involves to exploitthe specific structure of the problem at hand. On theother hand, we discuss the inherent optimization and glob-alization properties of the multigrid optimization method(MGOPT) where the multigrid solution framework definesthe outer loop of classical optimization schemes. This ap-proach can be successfully applied to problems with verydifferent structure.

Alfio BorziInstitute of MathematicsUniversity of Graz, Austriaalfio.borzi@uni-graz.at

MS62

Multilevel Methods for Constrained Image Regis-tration

In this work we present a new and general frameworkfor image registration when having additional constraintson the transformation. We demonstrate that registrationwithout constraints leads to arbitrary results depending onthe regularization and in particular produces non-physicaldeformations. Having additional constraints based on theimages introduces prior knowledge and contributes to reli-ability and uniqueness of the registration. In particular weconsider optimization techniques for the recently proposedlocally rigid transformations. In contrast to existing ap-proaches, we propose a constraint optimization frameworkand do not rely on penalty methods that do not guaranteefeasible solutions.

Eldad HaberEmory UniversityDept of Math and CShaber@mathcs.emory.edu

MS62

Automatically Assessing the Performance of AnOptimization-Based Multigrid Method

Many large nonlinear optimization problems are basedupon discretizations of underlying continuous functions.Optimization-based multigrid methods are designed tosolve such discretized problems efficiently by taking ex-plicit advantage of the family of discretizations. The meth-ods are generalizations of more traditional multigrid meth-ods for solving PDEs. We discuss techniques whereby themultigrid method can assess its own performance, with thegoal of automatically determining whether the optimiza-tion model is well suited for the multigrid-type algorithm.

Michael LewisCollege of William and Marybuckaroo@math.wm.edu

Stephen G. NashGeorge Mason UniversitySchool of Information Technology & Engineeringsnash@gmu.edu

122 OP08 Abstracts

MS62

A Line Search Multigrid Method for Large-ScaleNonconvex Optimization

We present a line search multigrid method based on Nash’sMG/OPT multilevel approach for solving discretized ver-sions of general unconstrained infinite dimensional opti-mization problems. Introducing a new condition to a back-tracking line search procedure, the step generated fromthe coarser levels is guaranteed to be a descent direction.Global convergence is proved under fairly minimal require-ments on the minimization method used at all grid levels.In particular, our proof does not require that these mini-mizations, or so-called “smoothing” steps, which we inter-pret in the context of optimization, be taken at each gridlevel in contrast with multigrid algorithms for PDEs, whichfail to converge without such steps. Preliminary numericalexperiments show that our method is promising.

Donald Goldfarb, Zaiwen WenColumbia Universitygoldfarb@columbia.edu, zw2109@columbia.edu

MS63

Optimizing Control of SMB Processes with End-point Constraints

Endpoint constraints in the form of terminal sets are a nec-essary ingredient for guaranteed stability of moving hori-zon optimizing control strategies. We describe an applica-tion of this concept to Simulated Moving Bed Processes.In addition to minimizing a cost function over the predic-tion horizon, the terminal state is driven to a shrinkingset around the optimal steady state operating point. Therequired product purity is imposed as a constraint in theoptimization.

Sebastian EngellUniversity of DortmundGermanysebastian.engell@bci.uni-dortmund.de

Achim KuepperDept. of Biochemical and Chemical EngineeringUniversity of DortmundAchim.Kuepper@bci.uni-dortmund.de

Pham Le-ChiUniversity of Dortmundle-chi.pham@bci.uni-dortmund.de

MS63

Free Boundary Control in a Viscous Flow Problem

Considering a viscous inertial Newtonian fluid in an opencontainer, the goal of this work is to move the container outoff the stand over a certain distance in a given time whilekeeping the surface smooth and avoiding overflow. Thetransport of the fluid in the open container is modelled bya free boundary value problem in terms of incompressibleNavier-Stokes equations in moving coordinates with no-slip conditions at the walls and kinematic and dynamicboundary conditions at the free surface. The formulation

of the free boundary as graph enables its access to thestate variables. Thus, we end up with an pde-constraintoptimization problem for the free surface, fluid velocity andpressure – while the outer transport speed acts as control– for which numerical results are presented.

Nicole MarheinekeTechnical University Kaiserslauternnicole@mathematik.uni-kl.de

MS63

Recent Advances in Optimal Dopant Profiling forSemiconductor Devices

We present some recent advances for optimal dopant pro-filing of semiconductor devices. Escpecially, we discuss theconvergence of a generalized Gummel algorithm and show anew approach to solve multi-objective optimal design ques-tions. Both techniques can be easily implemented into ex-isting semiconductor device simulation tools.

Rene PinnauTechnische Universitat KaiserslauterFachbereich Mathematikpinnau@mathematik.uni-kl.de

MS63

Parameter Estimation in Calcium Signaling to theNucleus of Neurons

Signal processing in neurons takes place on different levels.For one, electrical signals are propagated in the dendritictree, towards or away from the soma. Secondly, electricalinformation that reaches the soma is partially recoded as acalcium wave that propagates towards and into the cell nu-cleus, activating biochemical reactions which result in theexpression of certain genes. To address both signal process-ing in the dendritic tree of the neuron and calcium signalingat the cell nucleus, we have developed three dimensionalvolume models based on reconstructed 3-D geometries ofneurons and of neuron cell nuclei on which PDEs describethe underlying signaling processes. Embedded in theseequations are a number of parameters, such as neuronalmembrane capacitance, inner- and outer-neuronal capaci-tance or diffusion parameters for nuclear calcium. Basedon a full 3-D model and experimental data, e.g. recordedfrom laser-assisted calcium uncaging experiments, inversmodels are being developed in order to estimate key pa-rameters in the underlying PDEs. Here we make use ofNewton-like and SQP methods which are implemented inour simulation environment UG.

Gabriel Wittum, Gillian QueisserUniversity of Heidelbergwittum@iwr.uni-heidelberg.de, Gillian.Queisser@iwr.uni-heidelberg.de

MS64

An Open Source Exact Solver for Mixed IntegerNon-Linear Programming Problems

We discuss a spatial branch-and-bound algorithm for non-convex MINLP problems, based on a reformulation tech-

OP08 Abstracts 123

nique for factorable programs. The reformulation libraryis implemented as a cut generator and is available withinthe Coin-OR framework (www.coin-or.org). We presentthe features of our approach, such as novel branching rulesand bound tightening techniques, and show computationaltests on instance libraries such as GlobalLib and MinlpLib,and on other instances from industrial applications.

Pietro BelottiCarnegie Mellon UniversityTepper School of Businessbelotti@andrew.cmu.edu

Andreas WaechterIBM T.J. Watson Research Centerandreasw@us.ibm.com

Francois MargotCarnegie Mellon UniversityTepper School of Businessfmargot@andrew.cmu.edu

Jon Lee, Laszlo LadanyiIBM T.J. Watson Research Centerjonlee@us.ibm.com, ladanyi@watson.ibm.com

Ignacio GrossmannDept. of Chemical EngineeringCarnegie Mellon Universitygrossmann@cmu.edu

Larry BieglerCarnegie Mellon Universitylb01@andrew.cmu.edu

Pierre BonamiIBM TJ Watson Research Centerpbonami@us.ibm.com

MS64

Primal Heuristics of the Branch-Cut-and-Price-Framework SCIP

In modern MIP-solvers like the state-of-the-art open sourcebranch-cut-and-price framework SCIP, primal heuristicsplay a major role in finding and improving feasible solu-tions at the early steps of the solution process. We give anoverview about different categories of heuristics, present anew large neighborhood search heuristic and an improvedversion of the feasibility pump.

Timo BertholdZuse Institute, Berlinberthold@zib.de

MS64

MIQCP: In Between QCP and MILP

A natural approach for solving Mixed Integer Quadrat-ically Constrained Programs (MIQCP) is to solve aQuadratically Constrained Program (QCP) at each nodein the tree. An alternative is to solve them as MILP us-ing branch and cut. In this talk we will be describe and

compare both approaches which are now implemented inILOG CPLEX.

Christian BliekILOG CPLEXbliek@ilog.fr

MS64

State-of-the-Art in Linear and Nonlinear MIP

Abstract not available at time of publication.

Hans D. MittelmannArizona State UniversityDepartment of Mathematics and Statisticsmittelmann@asu.edu

MS65

The Difference Between 5x5 Doubly Nonnegativeand Completely Positive Matrices

The convex cone of n×n completely positive (CPP) matri-ces and its dual cone of copositive matrices arise in severalareas of applied mathematics, including optimization. Ev-ery CPP matrix is doubly nonnegative (DNN), i.e., positivesemidefinite and component-wise nonnegative. Moreoverfor n ≤ 4, every DNN matrix is CPP. We investigate thedifference between 5× 5 DNN and CPP matrices. We givea precise charaterization of how a 5×5 DNN matrix that isnot CPP differs from a DNN matrix, and use this charater-ization to show how to separate an extreme DNN matrixthat is not CPP from the cone of CPP matrices.

Kurt M. AnstreicherUniversity of IowaDepartment of Management Scienceskurt-anstreicher@uiowa.edu

Samuel BurerUniversity of IowaDept of Management Sciencessamuel-burer@uiowa.edu

Mirjam DuerTU Darmstadtduer@mathematik.tu-darmstadt.de

MS65

On the Copositive Representation of Binary andContinuous Nonconvex Quadratic Programs

A recent line of research has shown that a small collec-tion of NP-hard quadratic optimization problems can berepresented as linear programs over a specific convex set(the cone of completely positive matrices). Although suchconvex programs are necessarily NP-hard, their structureallows them to be approximated in a mechanical way upto any accuracy by linear and semidefinite programs. Wereview these results and then, in the main portion of thetalk, show that any nonconvex quadratic program having amix of binary and continuous variables (for example, all 0-1integer programs) can be represented in the above fashion.This can be viewed as a broad extension of the aforemen-

124 OP08 Abstracts

tioned earlier results.

Samuel BurerUniversity of IowaDept of Management Sciencessamuel-burer@uiowa.edu

MS65

An Adaptive Algorithm for Copositive Programs

We consider linear programs over the cone of copositivematrices which arise in integer and nonconvex quadraticprogramming. We introduce copositivity conditions whichwe use to define polyhedral inner and outer approximationsof the copositive cone. From these, we derive an adaptivelinear approximation algorithm for copositive problems. Incontrast to previous approaches, our approximation is notuniform but adaptively guided by the objective function.Numerical experience with the algorithm is presented.

Mirjam Duer, Stefan BundfussTU Darmstadtduer@mathematik.tu-darmstadt.de,bundfuss@mathematik.tu-darmstadt.de

MS65

Semidefinite and Linear Relaxation Schemes forthe Copositive Cone

We propose various semidefinite and linear programmingrelaxations of the copositive cone. We then examine thetradeoffs in the quality of the relaxations and their compu-tational cost. We rely on the copositive formulation of thestability number of a graph as a benchmark for assessingthe quality of the different relaxations.

Javier PenaCarnegie Mellon Universityjfp@andrew.cmu.edu

Juan VeraUniversity of Waterloojuancavera@gmail.com

Luis ZuluagaUniversity of New Brunswicklzuluaga@unb.ca

MS66

Probabilistic Analysis of LP

We give an overview of the literature on the probabilisticanalysis of linear programming from the early 1980-ies tothe present, and we discuss the explanatory power of theseresults and desirable extensions thereof.

Raphael A. HauserOxford University Computing Laboratoryhauser@comlab.ox.ac.uk

MS66

Recent Progress in Primal-Dual Methods for Con-

vex Optimization

I will review some of the new developments in the theory ofprimal-dual interior-point algorithms for convex optimiza-tion in the context of recent history of the modern interior-point methods. I will focus on some breakthroughs in thearea and their theoretical evolution as well as impact.

Levent TuncelUniversity of WaterlooDept. of Combinatorics and Optimizationltuncel@math.uwaterloo.ca

MS66

Optimization and Quantitative Portfolio Manage-ment

Optimization models and methods are central elements ofquantitative equity portfolio management platforms. Theyserve as sophisticated tools for transfering the excess returnideas generated through research and testing into portfo-lios that best represent these ideas. In addition to thestandard mean-variance optimization models that are ad-justed for trading costs, we will discuss topics such asmulti-portfolio optimization (optimizing multiple portfo-lios simultaneously while minimizing the joint market im-pact costs) and multi-period portfolio selection.

Reha TutuncuGoldman SachsReha.Tutuncu@gs.com

MS66

Two Algorithms for the Minimum Enclosing BallProblem

Given A := {a1, . . . , am} ⊂ Rn and ε > 0, we proposeand analyze two algorithms for the problem of comput-ing a (1 + ε)-approximation to the radius of the minimumenclosing ball of A. The first algorithm is closely relatedto the Frank-Wolfe algorithm with a proper initializationapplied to the dual formulation of the minimum enclosingball problem. We establish that this algorithm convergesin O(1/ε) iterations with an overall complexity bound ofO(mn/ε) arithmetic operations. In addition, the algorithmreturns a “core set” of size O(1/ε), which is independent ofboth m and n. The latter algorithm is obtained by incor-porating “away” steps into the former one at each iterationand achieves the same asymptotic complexity bound as thefirst one. While the asymptotic bound on the size of thecore set returned by the second algorithm also remains thesame as the first one, the latter algorithm has the potentialto compute even smaller core sets in practice since, in con-trast with the former one, it allows “dropping” points fromthe working core set at each iteration. Our computationalresults indicate that the latter algorithm indeed returnssmaller core sets in comparison with the first one. We alsodiscuss how our algorithms can be extended to computean approximation to the minimum enclosing ball of otherinput sets. In particular, we establish the existence of acore set of size O(1/ε) for a much wider class of input sets.

Emre Alper Yildirim

OP08 Abstracts 125

Bilkent Universityyildirim@bilkent.edu.tr

MS67

Applications Where GSS Methods are able to Copewith Nonsmoothness

We consider minimization problems where the objectivefunction is piecewise smooth on a finite family of polyhe-dra. Problems of this kind arise in many areas of appliedsciences, like for example in signal and image restoration,financial mathematics or multivariate data analysis. Someof these problems are in fact piecewise linear and can besolved by linear programming techniques; in other caseshowever, reformulations as linear programs are impossiblebecause of nonlinear terms in the objective function. Gen-erating set search methods represent a direct and somehownatural approach to cope with this type of nonsmoothness.

Claudio BoganiUniversity of Birminghamboganic@maths.bham.ac.uk

Maria Grazia Gasparo, Alessandra PapiniDipartimento di Energetica ‘S. Stecco’Univerity of Florencemgasparo@unifi.it, apapini@unifi.it

MS67

Assessing Polymer Extrusion Filter Performancewith Gradient-Free Optimization Methods

Debris filtration is an important component of the poly-mer fiber melt-spinning process. Filters are replaced oncea significant amount of debris accumulates inside the filtra-tion medium; manufacturers also want a minimal amountof debris in the finished product. As each event carries anassociated cost, we measure filter performance by combin-ing these objectives. We use a simulation tool to evalu-ate our functional, thus necessitating the use of derivative-free methods to find parameters that optimize filter per-formance.

Lea JenkinsDepartment of Mathematical SciencesClemson Universitylea@clemson.edu

Kathleen FowlerClarkson Universitykfowler@clarkson.edu

MS67

Optimal Design of Municipal Water Supply Port-folios with Implicit Filtering

In this talk we describe an application of implicit filteringto water resources management. The problem is the opti-mal design of a portfolio of water rights, leases, and optionsbased on a stochastic model of the water supply. The re-liability and conditional value at risk of the design lead toconstraints which can only be tested after the simulation is

complete. We can estimate the noise in the function withprobabilistic methods and use that information to controlthe cost of the optimization.

Tim KelleyNorth Carolina State UnivDepartment of Mathematicstim kelley@ncsu.edu

Karen DillardAir Force Institute of Technologykdillard1@nc.rr.com

Brian Kirsch, Greg CharacklisUniversity of North Carolinabkirsch@email.unc.edu, charack@email.unc.edu

MS67

Challenges in Using Derivative-Free OptimizationMethods for Scientific Applications

Optimization has taken an increasingly larger role in manyscientific problems today. This is due in large part to therapid rise of computational modeling and simulation inmany scientific fields. As a result, many scientists are nowstarting to consider using optimization for problems suchas the determination of the surface structure of nanosys-tems, fitting supernova models to data, and the design andoperation of particle accelerators. All of the problems sharethe property that no derivative information is readily avail-able. In this talk, I will discuss some of the challenges andthe approaches we have taken for addressing optimizationproblems arising from these applications.

Juan C. MezaLawrence Berkeley National Laboratorymeza@hpcrd.lbl.gov

MS68

A Stochastic Multiple-Leader Stackelberg Model:Analysis, Computation, and Application

We study an oligopoly consisting of multiple leaders andmultiple followers that supply a homogeneous product non-cooperatively. Leaders choose their supply levels first,knowing the demand function only in distribution. Fol-lowers make their decisions after observing the leader sup-ply levels and the realized demand function. We show theexistence and uniqueness of equilibrium, propose a compu-tational approach based on the sample average approxima-tion method, and apply this framework to model competi-tion in the telecommunication industry.

Victor DemiguelLondon Business Schoolavmiguel@london.edu

Huifu XuSouthampton Universityh.xu@soton.ac.uk

126 OP08 Abstracts

MS68

Loss of Efficiency in Quadratic Utility Games

We study quadratic utility games (for example, Cournot,i.e. quantity competition). We first consider an affinedemand-price relation. We present a bound on the lossof efficiency (ie. comparison of system profit between cen-tralized and decentralized settings) that depends on thenumber of players and the maximum market power of theplayers. We discuss a setting where sellers have lack ofinformation on the other sellers’ constraints. As a result,we provide a bound that is independent of the constraintsof the game. Our results apply to competition where mul-tiple products share capacities. We further generalize ourresults to classes of nonlinear demand functions as well asmore general measures of efficiency.

Jonathan Kluberg, Georgia PerakisMITkluberg@mit.edu, georgiap@mit.edu

MS68

A New Stochastic Game: 2-Stage Perfect Compe-tition with Endogenous Probabilities

Abstract not available at time of publication.

Danny RalphJudge Institute of Cambridgedr241@hermes.cam.ac.uk

MS68

Empirical Pricing Game with Multiple Equilibria

We study a Bertrand oligopoly with random coefficientslogit demand model. For a given set of parameters, ourmodel would generate multiple price equilibria. We pro-pose an MPEC approach to estimate structural parametersin this model and show that our approach is computation-ally faster than the widely-used BLP estimator.

Jean-Pierre DubeChicago GSBjdube@chicagogsb.edu

Che-Lin SuKellogg School of Managementc-su@kellogg.northwestern.edu

Maria Ana VitorinoChicago GSBmvitorin@chicagogsb.edu

MS69

Optimization and Inverse Modeling in MetricSpaces

Reservoir modeling and management calls for the applica-tion of non-linear optimization in a highly dimensional anduncertain/stochastic parameter space (the reservoir modelspace). In this presentation, I formulate the stochastic op-timization problem in a metric space defined by a distancebetween any two model realizations. Using this metric

space, we can reformulate the modeling or optimizationproblems in a much lower dimension, hence apply stan-dard gradient-based or stochastic optimization techniqueseffectively.

Jef CaersDepartment of Energy Resources EngineeringStanford Universityjcaers@Stanford.edu

MS69

Inverse Modeling of Oil Reservoirs Using Inte-grated Data

The mathematical models used for forecasting oil produc-tion involve geological parameters that must be tuned us-ing field data in order to provide meaningful predictions.This calibration process yields large-scale inversion prob-lems that in general have nonunique optimal solutions. Inthis talk we regularize these problems by jointly consideringfield data of different kinds, namely cross-well tomographicdata and flow measurements. We demonstrate that the useof these two data types provides more realistic geologicalparameters.

David Echeverria-CiaurriDepartment of Energy Resources EngineeringStanford Universityecheverr@stanford.edu

Eduardo SantosDepartment of GeophysicsStanford Universityeduardot@stanford.edu

Khalid Aziz, Louis J. DurlofskyDepartment of Energy Resources EngineeringStanford Universityaziz@stanford.edu, lou@stanford.edu

Jerry M. Harris, Tapan MukerjiDepartment of GeophysicsStanford Universityjerry.harris@stanford.edu, mukerji@stanford.edu

MS69

Flooding Optimization of Oil Reservoirs

We consider model-based techniques to optimize produc-tion from oil reservoirs by changing well operating parame-ters over the full producing life of the reservoir. The modelsconsist of discretized nonlinear diffusion-convection equa-tions. The optimization methods are gradient-based usingan adjoint formulation. The large number of control pa-rameters makes the problem-ill posed and we discuss vari-ous strategies to regularize the problem.

Jan Dirk JansenDelft University of Technology, andShell Exploration and Productionj.d.jansen@citg.tudelft.nl

OP08 Abstracts 127

MS69

Efficient Ensemble-Based Closed-Loop ProductionOptimization

In this paper, we describe a new method for closed-loop op-timization, which combines ensemble-based optimizationwith the Ensemble Kalman Filter (EnKF) for data assim-ilation. The EnKF adjusts the reservoir models to honorobservations and propagates the uncertainty in time. Anensemble-based steepest ascent method is used to optimizethe expectation of the net present value based on the up-dated reservoir models. The method is illustrated with awaterflood example.

Yan Chen, Dean S. Oliver, Dongxiao ZhangMewbourne School of Petroleum and GeologicalEngineeringThe University of Oklahomayan@ou.edu, dsoliver@ou.edu, donzhang@ou.edu

MS70

Ab Initio Molecular Dynamics and ElectronicStructure Simulations That Involve Thousands ofAtoms: Algorithmic, Numerical and High Perfor-mance Computing Challenges

Electronic structure calculations from first principles haverevealed a remarkable wealth of information concerning im-portant properties of materials and nano-structures. Tak-ing advantage of the advances in computing (softwareand hardware) and the advent of massive parallelism thefuture looks even more promising. We will show thatmoving to next generation simulations with tens of thou-sands of atoms requires the efficient combination of power-ful optimization and numerical algorithms with the latestparadigms of parallel computing.

Costas BekasIBM Research DivisionZurich Research LaboratoryBEK@zurich.ibm.com

MS70

Iterative Algorithm for Wave Functions Optimiza-tion in Density Functional Theory: Inexact Newtonwith Anderson Acceleration

We put a mathematical framework around a numerical al-gorithm we have used to solve electronic structure problemsin recent years. The approach is described as a subspaceaccelerated inexact Newton inspired by Fokkema et al. Itmakes use of the acceleration scheme introduced by Ander-son. It is applicable in O(N) algorithms where electronicorbitals are confined to localization regions.

Jean-Luc FattebertLawrence Livermore National Lab.fattebert1@llnl.gov

MS70

Experience with Gradient-Based OptimizationMethods for Energy Minimization in Electronic

Structure Calculations

The problem of finding mechanically stable configurationsof materials is a common task in computational materi-als science, physics, chemistry, and biology. This corre-sponds to finding the nearest material configuration, withminimimum potential energy, from a given configuration.There are many well-established gradient-based optimiza-tion methods (including quasi-Newton, conjugate gradient,and others) available for this task. In this talk, we considersuch methods and compare results obtained from usingthese methods to find mechanically stable material con-figurations.

Suzanne M. ShontzDepartment of Computer Science and EngineeringThe Pennsylvania State Universityshontz@cse.psu.edu

Yousef SaadDepartment of Computer ScienceUniversity of Minnesotasaad@cs.umn.edu

MS70

Numerial Algorithms for Total Energy Minimiza-tion in Electronic Structure Calculation

One of the fundamental problems in electronic structurecalculations is to determine the electron density associatedwith the minimum total energy of a molecular or bulk sys-tem. The total energy minimization problem is often for-mulated as a nonlinear eigenvalue problem and solved byan iterative procedure called the self-consistent field (SCF)iteration. In this talk, I will describe SCF and explain whyit can fail to converge. I will discuss techniques for im-proving the convergence of SCF and present an alternativealgorithm that minimizes the total energy directly.

Chao YangLawrence Berkeley National LabCYang@lbl.gov

MS71

OB1: The Computational History

In 1988, Lustig, Marsten and Shannno began a collabora-tion to develop OB1, which was used to develop numerousinsights into the computational aspects of primal-dual in-terior point methods for linear programming. In this talk,we will review the history of these developments and itsimpact on computational linear programming.

Irv LustigILOGilustig@ilog.com

MS71

Lagrangian Transformation in Constrained Opti-mization

A class of strongly concave and smooth enough functionsψ : � → � is used for transforming terms of the Classical

128 OP08 Abstracts

Lagrangian related to constraints. The resulting functionis used for developing two classes of multipliers methods.The first class is equivalent to the Interior Prox methodswith Bregman distance function for the dual problem whilethe second is equivalent to the Interior Quadratic Prox inthe rescaled dual space. We use the equivalence for provingconvergence and estimating the rate of convergence of themultipliers methods.

Roman PolyakDepartment of SEOR & Math SciencesGeorge Mason Universityrpolyak@gmu.edu

MS71

Using MPECs to Derive Implied Binomial Trees

It is widely recognized that the assumption of constantvolatility in the Black-Scholes options pricing model is in-correct. One way to modify Black-Scholes is to use a modelwith local volatility. However, in the case of Amercian op-tions, deriving the implied parameters for a binomial treewhen volatility is no longer assumed to be a constant provesto be a difficult proposition, with much attention given inthe literature. Here we consider an approach to derivingimplied binomial trees by solving a mathematical programwith equilibrium constraints, or MPEC.

Arun SenNERA Economic Consultingarun.sen@nera.com

MS72

A PDE-Constrained Approach to Electrostatic Op-timization of Biomolecules

A convex quadratic program has been derived for opti-mizing the electrostatic component of binding free ener-gies between molecules, and experimental validation ofthe formalism has demonstrated its usefulness in molec-ular analysis and design. We have developed a novelPDE-constrained formulation that dramatically reducesthe computational cost for these problems, outperformingthe original method and also standard PDE-constrainedtechniques. Biological examples demonstrate the method’sviability and performance, as well as issues faced generallyby PDE-constrained approaches.

Jaydeep P. BardhanMathematics and Computer Science DivisionArgonne National Laboratoryjbardhan@alum.mit.edu

MS72

Optimization Methods in Applied Protein Design

The definition of an appropriate inverse problem to theprotein structure prediction problem, coupled with the ap-plication of remarkably effective tree pruning and searchalgorithms, has made computational protein design a re-ality. Here, we will discuss the optimization techniquesunderyling applied protein design, as well as an applica-tion involving the simultaneous design of optimal genetic

(DNA) and amino-acid sequences for expressed natural orartificial proteins.

David GreenDepartment of Applied Mathematics and StatisticsState University of New York, Stony Brookdfgreen@stonybrook.edu

MS72

Monte Carlo-Based Prediction of Ligand BindingGeometries

A wealth of computational strategies is available for pre-dicting the binding site and affinities of a putative ligandinside a target receptor. Although numerous techniqueshave been reported for the orientation of ligands or frag-ments thereof, few methods have delved into improving theaccuracy of generating reliable ligand conformations withinpredicted binding modes. In an effort to comprehensivelysample the torsion space available to a flexible ligand andfocus on low energy conformations, a recursive, Metropo-lis Monte Carlo-based rotamer design protocol has beendeveloped. This approach recursively samples adjacent ro-tatable bonds from a defined anchor and directs the searchalong low energy pathways, such that high-affinity confor-mations of the ligand can be identified. Furthermore, thisprogram applies spatial constraints within the search thatrestrict the solutions to structurally dissimilar conforma-tions, thus encouraging diversity in the solution set. Theperformance of moleculeGL has been evaluated for a set of55 cocrystals, with the numberof rotatable bonds for theligands varying from 2 to 32. About 85% of the structurespredicted, starting from an arbitrary ligand conformation,are within 2.0 A2 root mean square displacement with re-spect to the crystal structure. This high level of accu-racy starting from arbitrary ligand conformation suggeststhe program’s applicability to the design of pharmacaphoresubstituents, for which the position of a chemically-activepharmacaphore is well-known.

Peter HuskeyCalifornia Institute of Technologyhuskeypm@wag.caltech.edu

MS72

Electrostatic Optimization in Drug and Drug Cock-tail Design

In this talk, I will outline two major optimization tech-niques as they apply to drug design. The first techniquedetermines the electrostatic properties of a hypotheticaldrug molecule that binds as tightly as possible to its target,using a continuum electrostatics framework. This methodhas been used to improve and analyze existing molecules,and it can potentially be used in design. The second tech-nique uses integer-programming based methods to select ordesign drug cocktails that can collectively target a rapidly-mutating agent. Such methods could be useful in a systemwith multiple target variants, such as HIV or certain formsof cancer. Finally, these two techniques can be combined tofurther understand the physical determinants of moleculesand drug cocktails capable of recognizing rapidly mutating

OP08 Abstracts 129

drug targets.

Mala RadhakrishnanDepartment of ChemistryWellesley Universitymradhakr@wellesley.edu

MS73

Shape Optimization for Biocompatibility in Im-plantable Blood Pump Design

Several challenges and methods in biomedical flow devicedesign are described. The objective often involves theunique behavior of blood as the flowing medium, neces-sitating, e.g., accurate modeling of cell damage. The com-plex constitutive behavior, in particular shear-thinning,may affect the outcome of shape optimization more thanit affects direct flow analysis. Finally, target applicationsoften involve intricate time-varying geometry, and thus, re-alistic solutions can be only obtained on high-performanceparallel computers.

Marek BehrRWTH Aachen UniversityChair for Computational Analysis of Technical Systemsbehr@cats.rwth-aachen.de

Stefanie Elgeti, Mike NicolaiRWTH Aachen Universityelgeti@cats.rwth-aachen.de, nicolai@cats.rwth-aachen.de

Markus ProbstRWTH Aachen UniversityChair for Computational Analysis of Technical Systemsprobst@cats.rwth-aachen.de

MS73

PDE Constrained Optimization with UncertainInput: Optimal Probe Location for the Radio-Frequency Ablation

The radio-frequency (RF) ablation is a promising mini-mally invasive treatment for lesions in the human liver:A probe containing electrodes is placed in the tumor andconnected to a generator. Consequently an electric currentflows through the tissue and heats it up to temperatures ofmore than 60 degrees Celsius. This leads to a coagulationof the cell’s proteins and thus a destruction of the malig-nant tissue. The success of the treatment heavily dependson a variety of patient-individual quantities, e.g. the localstructure of the vascular system and material parameterslike the water content of the tissue, its heat-capacity, itsheat- and electric-conductivity, etc. So in the interest ofthe patient a thorough planning of the therapy must bemade, yielding an optimal position and orientation of theprobe, and taking these important patient-individual prop-erties into account. The talk focusses on models for theoptimization of the RF-ablation. To take the uncertaintyassociated with patient individual material parameters intoaccount, we formulate the forward problem in terms of astochastic PDE. Consequently we consider objective func-tions which involve stochastic modes of the resulting proba-bility distribution of the heat distribution. We present the

corresponding optimality systems and an algorithm thatuses stochastic collocation to evaluate stochastic integrals.

Tobias PreusserCeVis, University Bremenpreusser@cevis.uni-bremen.de

MS73

Shape Optimization Under Uncertainty – AStochastic Programming Perspective

We present an algorithm for shape-optimization understochastic loading, and representative numerical results.Our strategy builds upon a combination of techniquesfrom two-stage stochastic programming and level-set-basedshape optimization. In particular, usage of linear elastic-ity and quadratic objective functions permits to obtain acomputational cost which scales linearly in the number oflinearly independent applied forces, which often is muchsmaller than the number of different realizations of thestochastic forces. Numerical computations are performedusing a level-set method with composite finite elementsboth in two and in three spatial dimensions.

Martin RumpfUniversitat Bonn, Germanyrumpf@math.uni-duisburg.de

MS73

Gradient Smoothing and Hessian Approximationfor Aerodynamic Shape Optimization in Oneshot

Numerical optimization in general and aerodynamic shapeoptimization in specific is a field which has seen muchprogress in the past decade. Since the adjoint approachmakes the computation of the gradient in principle inde-pendent of the number of design parameters, it is appealingto use a high resolution in the optimization process. Herewe parameterize the shape itself by the boundary meshnodes for the aerodynamic flow problem. This, however,may introduce high frequency noise in the shape, whichcan be circumvented by appropriate means. The Hessianfor these problems is usually a pseudo-differential operatorand knowledge of this operator can be used not only tocure the loss of regularity but also to accelerate the con-vergence of a gradient based optimization approach. Wepropose using the analytical shape derivative on the surfacenodes of the mesh, combined with the adjoint approach inthe flow field, which completely decouples the optimizationfrom the mesh generation. The implementational detailsand the efficiency of the resulting numerical methods foraerodynamic shape optimization are demonstrated in nu-merical examples of optimal wingcross-sections for Navier-Stokes flow.

Stephan SchmidtUniversity of TrierStephan.Schmidt@uni-trier.de

Volker SchulzUniversity of TrierDepartment of MathematicsVolker.Schulz@uni-trier.de

130 OP08 Abstracts

MS74

Solving Mixed-Integer Nonlinear Problems ofBlack-Box Type in Engineering Applications withSurrogate Functions

Simulation based optimization becomes increasingly im-portant in engineering applications, especially the needto handle real-valued as well as integer-valued variables isemerging. In this talk we give an introduction on this kindof optimization problems and present an optimization ap-proach based on sequentially updated surrogate functions.Numerical results obtained with the proposed approachwill be discussed for numerical examples from engineeringapplications where computational expensive, nonsmooth,black-box type mixed-integer nonlinear optimization prob-lems arise.

Thomas M. HemkerTechnische Universitat DarmstDepartment of Computer Sciencehemker@sim.tu-darmstadt.de

MS74

A Framework For Particle Swarm Optimization forMixed-Integer Problems Using Surrogate Models

Particle Swarm Optimization is a type of population based,heuristic optimization technique shown to perform well fornoisy, nonconvex objective functions containing many lo-cal minima. To improve the computational efficiency ofthe PSO algorithm, we propose a hybrid method that in-corporates a surrogate oracle to help update the swarmposition. Furthermore, since problems requiring popula-tion based methods are often expressed as mixed integerproblems, we also incorporate a modified PSO algorithmto directly handle integer variables.

Matthew ParnoClarkson Univeristyparnomd@clarkson.edu

Kathleen FowlerClarkson Universitykfowler@clarkson.edu

Thomas M. HemkerTechnische Universitat DarmstDepartment of Computer Sciencehemker@sim.tu-darmstadt.de

MS74

The Influence of Different Experimental Designson the Performance of ”Surrogate Model”-BasedSolvers

When dealing with costly (expensive to evaluate) objectivefunctions, one alternative is to use a surrogate model (re-sponse surface) approach. A common feature for all suchmethods is the need of an initial set of points, or ”exper-imental design”, in order for the algorithm to get started.The question is how to choose a good experimental design,since the behavior of the algorithms often depend heavily

on this set of initial points

Nils-Hassan Quttineh, Kenneth HolmstromDepartment of Mathematics and PhysicsMalardalen Universitynisse.quttineh@mdh.se, kenneth.homstrom@mdh.se

MS75

Interior Decomposition Methods for Two-StageStochastic Programming

We present theoretical and computational results on de-composition methods for solving two-stage stochastic pro-gramming problems. In particular, we show that thesemethods have the same first-stage worst case iteration com-plexity as their extensive formulation. Moreover, by intro-ducing a novel concept of self-concordant random variables,we show that under a probabilistic assumption the numberof iterations in a weighted decomposition method is inde-pendent of the number of scenarios. Additional theoreticaland computational results will be presented depending onthe progress.

Sanjay MehrotraIEMSNorthwestern Universitymehrotra@iems.northwestern.edu

MS75

Active Set Algorithms for Conic Programming

It is known that an upper bound can be placed on therank of an optimal solution to a semidefinite program. Anactive set method can then be designed which works withsemidefinite programs of size no larger than a small mul-tiple of this bound. We discuss approaches where a highdimensional cone is approximated by a lower dimensionalcone, with the lower dimensional cone updated from itera-tion to iteration.

John E. MitchellRensselaer Polytechnic Institute110, 8th Street, Troy, NY, 12180mitchj@rpi.edu

Kartik K. SivaramakrishnanNorth Carolina State UniversityDepartment of Mathematicskksivara@ncsu.edu

MS75

On Solving Specially Structured Large SDPs UsingIPMs

The stability conditions for spatially-distributed controlsystems give rise to large semidefinite programs with spe-cific block angular structure. The standard first-orderDantzig-Wolfe decomposition techniques are usually em-ployed. We explore related smooth counterparts that canbe solved using interior-point techniques whose subprob-lems are solved approximately and still promise fasterasymptotic convergence, as well as improved global con-

OP08 Abstracts 131

vergence.

Bharath RangarajanUniversity of Minnesotabharathr@me.umn.edu

MS75

A Parallel Interior Point Decomposition Algorithmfor Sparse Polynomial Optimization

Recently, Waki et al. have proposed a hierarchy of struc-tured semidefinite programming (SDP) relaxations in the”block-angular” form for sparse polynomial optimizationproblems. We discuss an interior point decomposition al-gorithm for solving these block-angular SDPs in a paralleland distributed high performance computing environment.We will also present our computational experiences withthe algorithm on the distributed ”Henry2” cluster at NCState University.

Kartik K. SivaramakrishnanNorth Carolina State UniversityDepartment of Mathematicskksivara@ncsu.edu

MS76

Improving the Homogeneous Self-Dual Interior-Point Method Via Projective Transformation

The homogeneous self-dual (HSD) embedding model isboth a theoretically interesting methodological tool as wellas a practical way to solve conic convex optimization prob-lems via interior-point methods (IPMs). Herein we studystopping rules for IPMs for the HSD model, and their impli-cations and connections to the complexity theory of conicconvex optimization. We also develop a projective trans-formation methodology for improving the theoretical per-formance of IPMs for solving HSD models. Computationalresults validate the practicality of our approach.

Robert M. FreundMITSloan School of Managementrfreund@mit.edu

Alexandre BelloniDuke UniversityFuqua School of Businessabn5@duke.edu

MS76

Bregman Iterative Algortihms for CompressedSensing and Matrix Rank Minimization

We propose efficient methods for solving the Basis Pur-suit problem min{‖u‖1 : Au = f, u ∈ R}, based on Breg-man iterative regularization, that obtain an accurate so-lution after solving only a very small number of instancesof the unconstrained problem minu μ‖u‖1 + 1

2‖Au− fk‖2

2.We prove that an exact solution is obtained in a finitenumber of steps, and present numerical results on hugecompressed sensing applications where matrix-vector op-erations involving A and AT can be computed by fast

transforms. We also, describe extensions to matrix rankminimization.

Don GoldfarbColumbia Universitygold@ieor.columbia.edu

Wotao YinRice Universityyin@rice.edu

Stanley J. OsherUniversity of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

Jerome DarbonMathematicsUCLAjerome@math.ucla.edu

MS76

Elimination of Free Variables for Solving Semidef-inite Programs Efficiently

An important issue in interior point methods for semidef-inite programs (SDPs) is handling of free variables. Re-cently, Kobayashi, Nakata, and Kojima proposed a methodthat transforms a given SDP with free variables into a stan-dard equality form SDP by eliminating free variables. Adisadvantage of the method is that the sparsity of the datamatrices of the SDP may be distroyed. We discuss howthe sparsity in the transformation can be maintained andshow some numerical results.

Masakazu KojimaTokyo Institute of Technologykojima@is.titech.ac.jp

Sunyoung KimEwha W. UniversityDepartment of Mathematicsskim@ewha.ac.kr

Hayato WakiTokyo Institute of Technologywaki9@is.titech.ac.jp

MS76

Competitive Market Equilibrium Computing

We present a fully polynomial-time approximation schemefor computing a symmetric Leontief economy equilibrium,that is, an exchange market equilibrium model with sym-metric Leontief’s utilities; where the equilibrium set can benon-convex and non-connected. We report our preliminarycomputational results using an interior-point potential re-duction algorithm for non-convex quadratic programming.

Yinyu YeStanford Universityyinyu-ye@stanford.edu

132 OP08 Abstracts

MS77

Parallel Derivative-free Non-Monotonous Algo-rithms for Bound Constraint Optimization

A new parallel algorithm is proposed that solves an opti-mization problem subject to bounds on the variables. Thealgorithm assumes no accurate derivative information, it isnon monotonous and converges under suitable assumptionsto a point satisfying the first order necessary condition foroptimality. Nonetheless, it includes ingredients to scapefrom local optima. The algorithm has three distinctiveproperties: a)A processor broadcasts only those points onwhich the processor is unable to make any improvement(partially blocked points), b)Directions of search are notassigned to processors. They look for improvement on agiven subspace, and c)Convergence is not impaired due toprocessors breakdowns. If only one processor is alive, it es-sentially executes a sequential algorithm. Preliminary nu-merical experiments on classical test problems are encour-aging. We noticed that the number of function evaluationsmay decrease when augmenting the number of processors.

Ubaldo Garcia-PalomaresUniversidad Simon BolivarVenezuelagarciap@usb.ve

Ildemaro Garcia-UrreaUniversidad Simon Bolivarijurrea@cantv.net

MS77

Adaptive Radial Basis Algorithms (ARBF) for Ex-pensive Global MINLP Optimization

Improvements of the adaptive radial basis function algo-rithm (ARBF) for computationally costly optimization arepresented. A new target value search algorithm and modifi-cations to improve robustness and speed are discussed. Thealgoritm is implemented in solver ARBFMIP in the TOM-LAB Optimization Environment (http://tomopt.com/).Solvers in TOMLAB are used to solve global and localsubproblems. Results and comparisons with other solversare presented for global optimization test problems. Per-formance on costly real-life applications are reported.

Kenneth HolmstromMalardalen Universitykenneth.holmstrom@mdh.se

Marcus EdvallTomlab Optimization Inc.medvall@tomopt.com

Nils-Hassan QuttinehDepartment of Mathematics and PhysicsMalardalen Universitynisse.quttineh@mdh.se

MS77

Extensions of Orbit to Computationally Expensive

Global Optimization

ORBIT (Optimization by Radial Basis Function Interpola-tion in Trust Regions) is an RBF model-based algorithm forunconstrained local derivative-free optimization of compu-tationally expensive functions. In this talk we explore pre-liminary extensions of ORBIT to the global optimizationsetting. The RBF models employed allow us to take advan-tage of previously-evaluated points, a particularly valuableproperty when the function of interest is computationallyexpensive. We will report on initial testing of some of theseextensions. -

Christine Shoemaker, Stefan WildCornell Universitycas12@cornell.edu, cas12@cornell.edu

MS77

Extension of Pswarm to Linearly ConstrainedDerivative-Free Global Optimization

PSwarm was developed originally for box-constrainedglobal optimization of functions without derivatives.PSwarm polls as in coordinate search and incorporates inthe search step a particle swarm scheme for disseminationand global optimization. PSwarm has just been extendedto handle general linear constraints. The poll step incorpo-rates now linear generators for the tangent cones includinga provision for the degenerate case. The search step hasalso been adapted accordingly. In particular, the initialpopulation for particle swarm is computed by first inscrib-ing an ellipsoid of maximum volume to the feasible set. Wehave again compared PSwarm to other global solvers andthe results confirm its competitiveness in terms of efficiencyand robustness. If time permits we will discuss the currentapplication of PSwarm to identify optimal parameters instar evolution models in astrophysics.

Luis N. VicenteUniversity of Coimbralnv@mat.uc.pt

A. Ismael F. VazUniversity of Minhoaivaz@dps.uminho.pt

MS78

Extended Mathematical Programs

Abstract not available at time of publication.

Michael C. FerrisUniversity of WisconsinDepartment of Computer Scienceferris@cs.wisc.edu

MS78

Generalized Disjunctive Programming and EMP

Abstract not available at time of publication.

Ignacio GrossmanCarnegie Mellon Universitygrossmann@cmu.edu

OP08 Abstracts 133

MS78

Dynamic Games and EMP

Abstract not available at time of publication.

Kenneth JuddHoover InstitutionStanford Universityjudd@hoover.stanford.edu

MS78

Modeling Extensions to Facilitate EMP in GAMS

Abstract not available at time of publication.

Alexander MeerausGAMS CorporationWashington, DCameeraus@gams.com

MS79

Optimization Problems in Energy Transmission

Oil and gas pipelines carry the bulk of the world’s energy,and are a rich source of challenging optimization prob-lems. Three common properties are: (A) Objectives andconstraints are derived from simulation software, (B) Thesimulation software itself may itself involve numerical so-lution of optimization problems, and (C) The results ofthe optimization are often needed directly, but in somedecision-making contexts they are of greatest value whenused quite indirectly. We present examples to illustrate theabove properties, and discuss a few useful algorithms andmethodologies to address some of the issues that arise inmulti-level optimization/simulation of this sort.

Richard CarterAdvantica Inc.richard.carter@advanticagroup.com

Sanjay YadavAdvanticasanjay.yadav@advanticastoner.com

MS79

How to Optimize a Complex Subsea Oil ProductionNetwork in the North Sea? Solving a Large-ScaleMINLP with a Combination of In-House and Com-mercial Tools

The Troll Oil field, located in the North Sea, is one of theworlds largest subsea developments. Present Troll produc-tion is governed by over 100 subsea wells, producing into27 clusters and with more than 200 kilometers flexible flowlines at water depths of 320 to 350 meters. Troll produc-tion is limited by the process gas-handling capacities andby flow line capacities. The main optimization variables inthe system are thus the choke valve positions, the gas liftrates, and the well routing. In mathematical terms, theproblem to be solved is a large-scale mixed-integer non-linear problem (MINLP). A system of in-house and com-mercial tools is used to model and solve this challengingproblem with satisfactory results. The system is currently

in use by the production engineers at the Troll field.

Marta Duenas-DiezStatoil-HydroNorwayMDD@StatoilHydro.com

MS79

Evaluation of Algorithms for Optimization of OilProduction

An important optimization problem in oil field operationsis the determination of optimal well settings (pressures,flow rates) to maximize oil production. In recent work weapplied gradient-based methods, with gradients obtainedfrom adjoint solutions, for these problems. These algo-rithms are efficient but require access to source code for theforward model and detailed code development. In this talk,we consider other algorithms for production optimizationand compare their performance with the adjoint procedure.

Lou DurlofskyEnergy Resources Engineering DepartmentStanford Universitylou@stanford.edu

David Ciaurri, Obi IseborStanford Universitydavid.echeverria@stanford.edu, oisebor@stanford.edu

MS79

Adjoint Calculations for a Reservoir ManagementProblem

We first present an optimization approach based on an al-gebraic surrogate model for the reservoir and outline itsstrength and deficiencies. Then we will present a modelderived from a PDE-based reservoir simulation. Finally,we demonstrate how to calculate adjoints and gradients fora time dependent optimal control problem using differenttime discretization schemes and present numerical results.

Klaus D. Wiegand, Amr El-BakryExxonMobil Upstream Research CompanyKlaus.D.Wiegand@exxonmobil.com,amr.s.el-bakry@exxonmobil.com

Matthias HeinkenschlossRice UniversityDept of Comp and Applied Mathheinken@rice.edu

MS80

Gossip Algorithms for Sensor Networks

Gossip algorithms have recently received significant atten-tion, mainly because they constitute simple and robust al-gorithms for distributed information processing over net-works. However, for many topologies that are realistic forwireless ad-hoc and sensor networks, the standard nearest-neighbor gossip is diffusive in nature and converges veryslowly. A series of recent results have successively im-proved the convergence time of such algorithms. This talk

134 OP08 Abstracts

will review this recent work, connections to eigenvalues oflarge random matrices, and further extensions to generalmessage passing algorithms for statistical inference in dis-tributed environments.

Alex DimakisEECS DepartmentUniversity of California at Berkeleyadim@EECS.Berkeley.EDU

Florence Benezit, Patrick ThiranEcole Polytechnique Federale de Lausanne (EPFL)florence.benezit@epfl.ch, patrick.thiran@epfl.ch

Martin VetterliEPFL, LausanneSwitzerlandMartin.vetterli@epfl.ch

MS80

Computing Sparse Generators of HomologyGroups in Simplicial Complexes

Computation of topological invariants of networks repre-sented by simplicial complexes have become a useful tool indiverse applications such as verification of dynamic cover-age in sensor networks and target enumeration. Simplicialcomplexes are the main object of study in algebraic topol-ogy and can be thought of as generalizations of graphs formodeling higher order relations, as opposed to just binaryones. One central step in applying such tools is comput-ing generators of homology groups which represent variouskinds of ”holes” in a network. In this talk, we presentan optimization based approach to distributed computa-tion of the sparsest generator for the homology groups ofsimplicial complexes. First we show how this problem isrelated to the problem of localizing coverage holes as wellas the problem of finding a minimal cover in a sensor net-work. Next, we show that the problem can be formulatedas an integer programming problem which can be relaxedto a linear program. We then show that the relaxation isexact, and therefore, one can efficiently compute the min-imal generator of the homology groups. We also present asubgradient method for finding the minimal generator in adistributed fashion.

Ali JadbabaieDepartment of Electrical and Systems EngineeringUniversity of Pennsylvaniajadbabai@seas.upenn.edu

Alireza Tahbaz-SalehiUniversity of Pennsylvaniaatahbaz@seas.upenn.edu

MS80

Distributed Multi-Agent Optimization

We present a distributed computational model for optimiz-ing a sum of convex objective functions corresponding tomultiple agents. In this model, each agent minimizes itsown local objective while exchanging the estimate infor-mation with the neighbors according to some rules. For

solving this (not necessarily smooth) minimization prob-lem, we consider a sub-gradient method that is distributedamong the agents. We study convergence properties andprovide convergence rate estimates for the method. Ourconvergence rate results explicitly characterize the tradeoffbetween a desired accuracy of the generated approximateoptimal solutions and the number of iterations needed toachieve the accuracy. We also study the effects of quanti-zation, and provide convergence results and rate estimatesfor a quantized method.

Angelia NedichDepartment of Industrial and Enterprise SystemsEngineeringUniversity of Illinois at Urbana-Champaignangelia@uiuc.edu

Asuman OzdaglarMassachusetts Institute of Technologyasuman@mit.edu

MS80

Matrix Splitting Methods for Distributed Opti-mization Problems

We consider the solution of distributed optimization prob-lems through the use of splitting approaches. Specifically,we provide conditions under which the subproblems insuch schemes can be solved using matrix splitting methods.Furthermore limited synchronization through linesearch ortrust region methods will be discussed. Some preliminarynumerical results are provided.

Uday ShanbhagDepartment of Industrial and Enterprise SystemsEngineeringUniversity of Illinois at Urbana-Champaignudaybag@uiuc.edu

ankur KulkarniUniversity of Illinois at Urbana-Champaignakulkar3@uiuc.edu

Angelia NedichDepartment of Industrial and Enterprise SystemsEngineeringUniversity of Illinois at Urbana-Champaignangelia@uiuc.edu

Asuman OzdaglarMassachusetts Institute of Technologyasuman@mit.edu

PP0

Optimization Method Applied to Analysis of Sur-face Water Quality in Eastern Massachusetts

The USGS National Water-Quality Assessment (NAWQA)Program provides long-term measurements on streams,rivers, ground water, and aquatic systems. Using time se-ries data from Eastern Massachusetts streams, we analyzethe current state of surface water, changes in time and de-pendence on land use, precipitation regime, and possible

OP08 Abstracts 135

other natural and human influences. We use optimizationtechniques to address the robustness of the statistical char-acterization of relationships among various measured dis-solved components and other physical parameters.

Constantin Andronache, Rudolph Hon, Qing Xian, BarrySchaudtBoston Collegeandronac@bc.edu, hon@bc.edu, xian@bc.edu,schaudt@bc.edu

PP0

Variational Formulation of Dynamic OligopolisticMarket Equilibrium Problem and ComputationalProcedure

The aim of the talk is to present a variational inequalityformulation of the dynamic oligopolistic market equilib-rium problem. Moreover existence theorems of a dynamicsolution to the associated evolutionary variational inequal-ity is showed under general assumptions and a continuitytheorem of the soluton is established. Then, we apply theregularity result to compute the solution of the dynamicoligopolistic market equilibrium problem by means a dis-cretization procedure.

Annamaria A. BarbagalloUniversity of CataniaDepartment of mathematics and Computer Sciencebarbagallo@dmi.unict.it

PP0

Competition and Efficiency in CommunicationNetworks

Kostas BimpikisDept of Electrical Engineering and Computer ScienceMITkostasb@mit.edu

Asu OzdaglarMITasuman@mit.edu

PP0

The Neos-Wiki – An Open-Access Online Opti-mization Resource.

The new NEOS-wiki places the ”NEOS Guide to Opti-mization”. The aim of the NEOS-wiki is to become a fo-cal point for optimization resources by extending the ex-tensive range of resources in the old guide, such as thecase studies, the optimization FAQs, and the softwareguide. This poster launches our campaign to encouragenew contributions from the optimization community. Seehttp://wiki.mcs.anl.gov/NEOS/

George BirosUniversity of Pennsylvaniabiros@seas.upenn.edu

Robert Fourer

Northwestern UniversityDepartment of Industrial Engineering and ManagementScience4er@iems.northwestern.edu

Sven LeyfferArgonne National Laboratoryleyffer@mcs.anl.gov

Jeff LinderothIndustrial and Systems EngineeringLehigh Universityjtl3@lehigh.edu

Jorge J. MoreArgone National Laboratorymore@mcs.anl.gov

Todd S. MunsonArgonne National LaboratoryMathematics and Computer Science Divisiontmunson@mcs.anl.gov

Jason SarichArgonne National Laboratorysarich@mcs.anl.gov

Stephen J. WrightUniversity of WisconsinDept. of Computer Sciencesswright@cs.wisc.edu

Henry WolkowiczDepartment of Combinatorics and OptimizationUniversity of Waterloohwolkowicz@uwaterloo.ca

PP0

A Primal-Dual Method for Nonlinear EqualityConstraints Programming

We analyze the behaviour of the Newton method appliedto a sequence of perturbed optimality systems that followfrom the quadratic penalty approach. We show that theusual requirement of solving the penalty problem at an ar-bitrary given precision may be replaced by a less stringentcriterion, while guaranteeing the global convergence. Lo-cal and global convergence results are presented, as well assome preliminary experiments.

Elsa BousquetUniversity of Limoges, Franceelsa.bousquet@etu.unilim.fr

Paul ArmandUniversite de LimogesLaboratoire XLIMpaul.armand@unilim.fr

Jol BenoistUniversity of Limoges, Francejoel.benoist@unilim.fr

136 OP08 Abstracts

PP0

An Improved Approximation Algorithm for theColumn Subset Selection Problem

Given A ∈ Rm×n and k n, the Column Subset SelectionProblem is: pick k columns from A to form C ∈ Rm×k,such that to minimize ||A−CC+A||ξ, for ξ = 2 or F. Thiscombinatorial optimization problem has been exhaustivelystudied within the numerical linear algebra and the the-oretical computer science communities. Current state-of-the-art approximation algorithms guarantee

||A− CC+A||2 ≤ O(k12 (n− k)

12 )||A−Ak||2,

||A− CC+A||F ≤√

(k + 1)!||A−Ak||F .Here, we present a new approximation algorithm whichguarantees

||A− CC+A||2 ≤ O(k34 log

12 (k)(n− k)

14 )||A−Ak||2,

||A− CC+A||F ≤ O(k√

log k)||A−Ak||F ,and asymptotically improves upon the previous results. Ak

is the best rank-k approximation to A, computed with theSVD

Christos BoutsidisComputer Science DepartmentRennselaer Polytechnic Instituteboutsc@cs.rpi.edu

Michael MahoneyYahoo! Researchmahoney@yahoo-inc.com

Petros DrineasComputer Science DepartmentRennselaer Polytechnic Institutedrinep@cs.rpi.edu

PP0

Greedy is Good, But Branching is Better: A Local-Ratio Style Improvement for Hitting Set of BundlesProblem

In this work, we extend the approximation analysis of theHitting Set of Bundles (HSB) problem using a greedy,rather than LP-based approach. This combinatorial frame-work yields a theorem, regarding the structure of the worst-case instances of HSB, that leads to a simple branchingimprovement scheme. We prove that this branching ap-proach yields the best-known approximation ratio on animportant class of HSB problems, and present experimen-tal results for more general instances.

Kevin M. ByrnesDepartment of Applied MathematicsJohns Hopkins Universitybyrnes@ams.jhu.edu

A.J. GoldmanJohn Hopkins Universitygoldman@ams.jhu.edu

PP0

A p-Cone Sequential Relaxation Procedure for 0-1Integer Programs

Given a 0-1 integer programming problem, several authorshave introduced sequential relaxation techniques – basedon linear and/or semidefinite programming – that generatethe convex hull of integer points in n steps. In this paper,we introduce a sequential relaxation technique based onp-order cone programming. We prove that our techniquegenerates the convex hull asymptotically and generalizesseveral existing methods. We also show that for p=2 ourmethod enjoys a better theoretical iteration complexity.

Sam Burer, Jieqiu ChenUniversity of Iowasamuel-burer@uiowa.edu, jieqiu-chen@uiowa.edu

PP0

Face Recognition Using Order-Value Optimization

Order-value optimization (OVO) is a generalization of theminimax problem; it consists in the minimization of thefunctional value that ranks in the p-th place. In this work,an application of OVO optimization to the problem of find-ing hidden patterns in data sets is described. In this appli-cation, one wants to identify a probe face image (rotation,scaling, and displacement) of a gallery (face set of knownfaces). Numerical experiments are presented.

Luziane F. De MendoncaDepartment of Computer ScienceFederal University of Rio de Janeiro - UFRJ - Brazilluziane@dcc.ufrj.br

PP0

Variational Shape Optimization with Applicationsin Image Processing

We describe a novel variational shape optimizationmethod, which closely follows the continuous structure ofthe geometric optimization problem. We express the ge-ometry explicitly and discretize the formulation with fi-nite elements. In this way we also easily incorporate spaceadaptivity to tune accuracy and computational cost. Adistinct feature of our method is the possibility to obtainspecially designed descent directions by varying the asso-ciated scalar products at the continuous level. We demon-strate our method in two image processing problems: thegeodesic active contour model for boundary detection andthe Mumford-Shah model for simultaneous image segmen-tation and smoothing.

Gunay DoganSchool of Engineering and Applied ScienceUniversity of Pennsylvaniagdogan@seas.upenn.edu

Pedro MorinDepartamento de MatematicaUniversidad Nacional del Litoral, Argentianpmorin@math.unl.edu.ar

Ricardo Nochetto

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Department of MathematicsUniversity of Maryland, College Parkrhn@math.umd.edu

PP0

Newton’s Method, Chebychev, Halley, and Beyondto Minimize f(x).

We present the classical Newton, Chebychev and (super)Halley iterative methods in the context of nonlinear un-constrained optimization. We observe that Newton’s andChebychev’s methods may be obtained from an extrapola-tion interpretation. On the other hand, both the Cheby-chev and Halley classical methods use similar expressionsinvolving third order derivative of the objective f. Wepresent fourth order methods inspired by those third or-der variants. For this poster presentation, we insist on theintuition underlying our developments.

Jean-Pierre Dussault, Bilel KchouckUniversite de SherbrookeJean-Pierre.Dussault@Usherbrooke.ca,bilel.kchouk@usherbrooke.ca

PP0

Multiple Return Estimation for Robust PortfolioOptimization

Classical mean-variance formulations for portfolio opti-mization problems depend on accurate and consistent esti-mates for expected returns and risks of securities includedin the portfolio selection model. A comparison of variousestimation techniques, however, shows that the predictedperformances typically vary widely and, thus, prompts torethink the concept of a robust portfolio. Using a multi-scenario multi-objective modeling approach that incorpo-rates several return estimates, new formulations for robustportfolio optimization are proposed and illustrated on ex-amples.

Alexander EngauUniversity of WaterlooDepartment of Management Sciencesaengau@uwaterloo.ca

PP0

Packing Cylinders on a Cylinder with Contact Con-straints

The problem of cylinder packing is investigated. The spe-cific problem is to find the optimal packing of congruentcylinders about a core cylinder of arbitrary dimensions.The constraint is that their circular face must keep in con-tact with the core cylinder. Mathematically, a lower andupper bound is determined. A quantitative result is alsofound using a modified genetic algorithm which reproducespublished results for the problem of packing congruent cir-cles within a circle.

Eric GooldCentral Michigan University, Department of Mathematicseric.goold@gmail.com

Leela RakeshCentral Michigan UniversityApplied Mathematics GroupLRakesh@aol.com

PP0

Approximation of Impulsive Solutions in FullyConvex Optimal Control Problems

Optimal control and calculus of variations problems withjoint convexity are considered, where the associated Hamil-tonian is possibly extended-real valued. As a consequence,optimal trajectories become arcs of bounded variation. Us-ing Goebel’s smoothing technique for the Hamiltonian,conditions under which solutions of the smoothed problemconverge to solutions of the original problem are identified.

Alvaro J. GuevaraLouisiana State UniversityDepartment of Mathematicsaguevara@math.lsu.edu

PP0

FDMA Based Optimality Analyses and Algorithms

Shunsuke HayashiDept of Applied Mathematics and PhysicsGraduate School of Informatics, Kyoto Universityshunhaya@amp.i.kyoto-u.ac.jp

PP0

Global Versus Local: An Analysis of the SelfishBehaviors in Spectrum Management

In this talk we shall discuss how each individual’s opti-mum behavior can alter the spectrum allocation in a mul-tiuser communication system. We show that if the usersrespond optimally to the *history* of the behavior of allother users, then the overall performance of the systemcan be improved. This suggests that it pays to educate theusers and manage the public information, notwithstandingthe selfish nature of the individual users. In other words,one kind of ”educated selfishness” may be better than theuninformed one, in the interest of global optimization.

Shuzhong ZhangThe Chinese University of Hong KongShatin, Hong Kongzhang@se.cuhk.edu.hk

Simai HeThe Chinese University of Hong KongHong Kong, Chinasmhe@se.cuhk.edu.hk

PP0

A One-Unit System Supported by a Spare and Ser-viced by Two Repair Persons

A one-unit system is supported by an identical spareunit, and is serviced at a facility where there is an in-house regular repair person who performs a perfect repair.

138 OP08 Abstracts

Should the repair take longer than a predetermined pa-tience time, or should the other unit also fail, immediatelyan expert repair person is called in to take over the re-pairing task. We call a model MER(multiple expert re-pair)/SER (single expert repair if the expert, once calledin, will fix all/only one failed unit before leaving. We useRPT(random pateience time)/DPT(deterministic patiencetime) to denote the case when the patience time is chosento be random/deterministic. Sridharan and Mohanavadivu(1998) proposed and study the SER-RPT model. We study4 models: MER-RPT, SRE-RPT, MER-DPT and SER-DPT and derive the optimal conditions for limiting avail-ability and profit per unit time for choices between these 4models.

Liang Hong, Jyotirmoy SarkarIndiana University - Purdue University Indianapolislihong@iupui.edu, jsarkar@math.iupui.edu

Bruno BiethDepartment of Mathematical SciencesIndiana University - Purdue University Indianapolisbbieth@math.iupui.edu

PP0

Optimization Approaches For The Inverse Elastic-ity Problem

This poster will focus on the inverse problem of identify-ing Lame parameters in elasticity. This problem has foundinteresting applications in elasticity imaging (in locatingcancerous tissues, and other abnormalities). We presentseveral optimization based approaches that can be used tosolve the inverse elasticity problem. Adaptive finite ele-ment methods are used in computations.

Baasansuren JadambaUnemployed at this timejadamba@hotmail.com

Akhtar A. KhanNorthern Michigan Universityakhan@nmu.edu

PP0

Identification of Transport Parameters of SoilsFrom Column Tests

Application of optimization techniques for identification oftransport parameters of soils: effective porosity, dispersiv-ity and sorption factors is discussed. The source of dataare results obtained from column tests for inert and sorb-ing ions migrating through different soils. The solutions ofpde problems are based on finite element method for non-steady transport. Different loading modes and models ofboundary conditions as well as scale effect are considered.

Mariusz Kaczmarek, K. Kazimierska-DrobnyKazimierz Wielki Universitymkk@man.poznan.pl, xxxx@man.poznan.pl

M. Marciniak, M. OkonskaA.Mickiewicz University

xxxx@xxx.xxx, xxx@xxx.xxx

PP0

Robust Optimization for Biological Network Cali-bration

Calibrating chemical-kinetics based differential equationmodels for biological networks is a task that is often madedifficult by the limited amount of available experimentaldata. When an additional robustness constraint is includedin the optimization problem, results suggest that the cali-bration can be made far less sensitive to a-priori parameterestimates. Research thus far has been conducted primarilyin the context of signal transduction pathways, such as themitogen-activated protein kinase pathway.

Bo S. KimResearch Laboratory of Electronics, MITDept. of Electrical Engineering and Computer Science,MITkaede11@mit.edu

Bruce TidorMITtidor@mit.edu

Jacob WhiteResearch Lab. of ElectronicsMITwhite@mit.edu

PP0

Pennon 1.0 - A Code for Nonlinear SemidefiniteProgramming

We will present PENNON 1.0 - the first release of the codefor solving mathematical optimization problems with realand matrix variables, smooth nonlinear (nonconvex) ob-jective and smooth nonlinear equality and inequality con-straints. All functions may depend on both types of vari-ables. Additionally, the matrix variables may be subject tospectral constraints, in particular, to positive semidefiniteconstraints. Matlab and extended AMPL interface allowthe user to formulate the problems easily. We will presenta few of numerous applications of the code.

Michal KocvaraSchool of MathematicsUniversity of Birminghamkocvara@maths.bham.ac.uk

Michael StinglInstitut fur Angewandte MathematikUniversitat Erlangen-Nurnberg, Germanystingl@am.uni-erlangen.de

PP0

Optimization of Cosmological Surveys

Due to the huge investment in next-generation Cosmo-logical surveys aimed at answering fundamental questionsabout the Universe, successful optimization of their designis vital. We consider an example, the optimization of the

OP08 Abstracts 139

$50M WFMOS survey, highlighting the impact of uniquelydeveloped algorithms for this purpose which involves mul-tiple design variables.

Jacques KotzeUniversity of Cape Townjacques@maths.uct.ac.za

Bruce BassettUniversity of Cape Town, South AfricaSouth African Astronomical Observatory, South Africabruce@saao.ac.za

PP0

FASTr: A Filter Active - Set Trust - Region Frame-work

We describe a new open-source library for solving large-scale nonlinear optimization problems. The library im-plements a flexible trust-region framework. Global con-vergence is promoted with a filter or a recently proposedtolerance tube. The framework includes SQP, SLP-EQP,and regularized LP methods, and allows a range of QP/LPsubproblem solvers. Numerical experience on the CUTErtest set is presented.

Sven LeyfferArgonne National Laboratoryleyffer@mcs.anl.gov

PP0

An Integrated Electric Power Supply Chain andFuel Market Network Framework: TheoreticalModeling with Empirical Analysis for New Eng-land

We develop a novel variational inequality-based electricpower supply chain network model with fuel supply mar-kets that captures both the economic transactions in en-ergy supply chains and the physical transmission con-straints in the electric power network. We then apply themodel to a specific large-scale case, the New England elec-tric power supply chain, consisting of 6 states, 5 fuel types,82 power generators, with a total of 583 power plant andgenerator combinations, and 10 demand market regions.We show that the model very closely predicts the actualprices.

Anna NagurneyIsenberg School of ManagementUniversity of Massachusetts, Amherst, MA 01003nagurney@gbfin.umass.edu

Zugang ”Leo” LiuUniversity of Massachusetts at Amherstzugang@acad.umass.edu

PP0

Comparison of Optimization Methods on theInverse Dynamics Musculoskeletal Problem inBiomechanics

A comparison study of a SQP and Gauss-Newton method is

presented for solving the inverse dynamics musculoskeletalproblem, formulated as an optimal control problem withdirect transcription. This kind of problem roughly consistsof computing muscle and reaction forces from motion data.Here the problem is formulated with objective function asthe least square difference between computed motion andmeasured motion and the equations of motion and muscledynamics equation as constraints.

Marie LundMid Sweden UniversityDeparment Engineering, Physics and Mathematicsmarie.lund@miun.se

Marten GullikssonMid Sweden UniversityDepartment Engineering, Physics and Mathematicsmarten.gulliksson@miun.se

PP0

An Interior Point Method for the Hydro PowerGeneration Scheduling with Nonlinear NetworkConstraints

Scheduling generation in hydro-thermal power systems isa large-scale, stochastic, nonlinear, and nondifferentiableproblem. Traditional modeling proposed so far inserts non-convexity, adding unecessary complexity to the problem.This work presents a new convex model that adds nonlin-earity to network constraints related to the electrical bal-ance equations. To solve the problem, an interior pointmethod that exploits particularities inherent to this classof problems is presented, drastically reducing the numberof matrix operations.

Leonardo MartinsFEEC/UNICAMPleonardo@cose.fee.unicamp.br

Anibal AzevedoSao Paulo State University at GuaratinguetaSchool of Engineeringatanibal@yahoo.com

Secundino Soares FilhoFEEC/UNICAMPdino@cose.fee.unicamp.br

PP0

Intelligent Robust Optimisation for Power Capac-ity Expansion

The aim of this study is to identify an optimised capacityexpansion plan for a power system based on future un-certain variables such as demand. To achieve this objec-tive, this research uses the concept of scenario planning toconsider different scenarios for the future. The proposedframework develops a scenario generator by using artificialneural networks and fuzzy logic. Then, an optimisationmethod called intelligent robust optimisation finds a robustinvestment option based on the different future scenarios.

Sorousha Moayer, Parisa Bahri, Ali Nooraii

140 OP08 Abstracts

Murdoch Universitys.moayer@murdoch.edu.au, p.bahri@murdoch.edu.au,ali.nooraii@alcoa.com.au

PP0

Subdifferentials Associated with Some Quasicon-vex Dualities

We study some subdifferentials for generalized convex func-tions, using some dualities and conjugacies. We establishsome links between concepts of generalized convexity andthese subdifferentials. We devise some optimality condi-tions for constrained optimization problems and the dualproblems. Key words: conjugate, duality, generalized dif-ferential, optimality conditions, subdifferential. Mathe-matics Subject Classification: 26B25, 49K26, 90C26

Linh T. NguyenUniversity of Natural Sciences, Ho Chi Minh City,Vietnamthin@princeton.edu

Christodoulos A FloudasDepartment of Chemical Engineering PrincetonUniversityNJ USAfloudas@titan.princeton.edu

PP0

An Efficiency Measure for Dynamic Networks withApplication to the Internet and Vulnerability Anal-ysis

We propose an efficiency measure for dynamic net-works, including the Internet, based on evolutionary vari-ational inequalities, which captures demands, flows, andcosts/latencies over time, and which allows for the iden-tification of the importance of the nodes and links andtheir rankings. We provide both continuous time and dis-crete time versions of the efficiency measure. We illustratethe efficiency measure for the time-dependent (demand-varying) Braess paradox and demonstrate how it can beused to assess the most vulnerable nodes and links interms of the greatest impact of their removal on the ef-ficiency/performance of the dynamic network over time.

Anna B. NagurneyUniversity of Massachusettsanna.nagurney@gbfin.umass.edu

Qiang ”Patrick” QiangUniversity of Massachusetts at Amherstqqiang@som.umass.edu

PP0

LSTRS: MATLAB Software for Large-Scale Trust-Region Subproblems and Regularization

We describe a MATLAB implementation of the LSTRSmethod proposed in M. Rojas, S.A. Santos and D.C.Sorensen. A new matrix-free algorithm for the large-scaletrust-region subproblem, SIAM J. Optim., 11(3): 611-646,2000. LSTRS is an iterative method that requires the solu-

tion of an eigenvalue problem at each step. The method islimited-memory and matrix-free. We describe the method,the software and present examples of its use as well as nu-merical results on large regularization problems.

Marielba RojasTechnical University of Denmarkmr@imm.dtu.dk

Sandra SantosState University of CampinasCampinas, Brazilsandra@ime.campinas.br

Danny SorensenRice UniversityHouston, Texassorensen@caam.rice.edu

PP0

A Solution for Large-Scale Nonlinear Least-Squares with Simple Bounds

We present an algorithm for bound-constrained nonlinearleast-squares that solves a sequence of bound-constrainedlinear least-squares subproblems. The subproblems arehandled efficiently by the subproblem solver. Comparedwith other constrained nonlinear optimization methods,this approach avoids forming the normal equations andonly requires matrix-vector products. Numerical experi-ments are presented to illustrate the effectiveness of thisapproach.

Shidong ShanUniversity of British Columbia, Canadashidong@cs.ubc.ca

Michael FriedlanderDepartment of Computer ScienceUniversity of British Columbiampf@cs.ubc.ca

PP0

Model-Based Optimal Control of Self-OrganizedBiochemical Systems

We demonstrate how model-based optimal control can beexploited in biological and biochemical modeling applica-tions focusing on the analysis and the target oriented ma-nipulation of self-organized dynamical systems. We showthat the formulation of inverse problems can provide im-portant insight into dynamic regulations of self-organizedcellular signal transduction. We apply mixed-integer opti-mization and Bock’s direct multiple shooting method to acircadian oscillator model. The resulting chronomodulatedpulse-stimuli schemes lead to restoration of the circadianrhythms.

Oliver SlabyCenter for Biosystem Analysisoliver.slaby@biologie.uni-freiburg.de

Sebastian Sager

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Interdisciplinary Center for Scientific Computingsebastian@sager1.de

Osman Shahi ShaikUniversity of California, Santa Barbaraxxxx@xxxx.xxx

Dirk LebiedzInterdisciplinary Center for Scientific ComputingUniversity of Heidelberg, Germanylebiedz@iwr.uni-heidelberg.de

PP0

Geometric Optimization on the Manifold of RankConstrained SPD Matrices

We present geometric optimization algorithms that approx-imate solutions of matrix equations by low-rank SPD ma-trices. By exploiting the fact that the set of rank con-strained SPD matrices is a smooth manifold, we can lift thecost function to the tangent space of the manifold. This al-lows us to circumvent the curse of dimensionality involvedin these matrix equations. The geometry and implemen-tation of the manifold as well as trust-region methods arediscussed.

Bart VandereyckenKatholieke Universiteit Leuvenbart.vandereycken@cs.kuleuven.be

Stefan VandewalleScientific Computing Research GroupKULeuvenstefan.vandewalle@cs.kuleuven.be

PP0

Environmental and Cost Synergy in Supply ChainNetwork Integration in Mergers and Acquisitions

In this paper, we quantify and assess, from a supply chainnetwork perspective, the environmental effects resultingwhen a merger or acquisition occurs and the resulting syn-ergy from possible strategic gains. We develop a multicrite-ria decision-making supply chain network framework thatcaptures the capacitated economic activities of manufac-turing, storage, and distribution pre and post the merger.The variational inequality-based models yield the systemoptima associated with the minimization of the total costsand the total emissions under firm-specific weights. Wepropose a synergy measure that captures the total general-ized cost. We then apply the new mathematical frameworkto quantify the synergy obtained for specific numerical ex-amples.

Anna NagurneyIsenberg School of ManagementUniversity of Massachusetts, Amherst, MA 01003nagurney@gbfin.umass.edu

Trisha WoolleyUniversity of Massachusetts at Amhersttwoolley@som.umass.edu

PP0

A Continuous Approach for Max K-Cut and Re-lated Zero-One Quadratic Programs

We give improved deterministic approximation scheme formax K-cut for small values of K. We also present a simplealgorithm for max K-cut which converges to a local optimalsolution. These approaches are extended to certain classesof zero-one quadratic programs, including the independentset problem.

Yu XiaSchool of MathematicsUniversity of Birminghamxiay@maths.bham.ac.uk

PP0

Analysis of Competitive Economy Equilibrium So-lution for Spectrum Management

This study analyzes the competitive economy equilibriumsolution for spectrum management in a weak-interferencemarket. Experimental results indicate that the competitiveeconomy equilibrium solution can provide an efficient spec-trum allocation to achieve a higher social utility and morenumber of users with higher individual utilities than theNash equilibrium solution in most cases. The approachesfor adjusting each users endowed monetary budget to im-prove the social utility and balance the individual utilitiesare also presented.

Yinyu YeStanford Universityyinyu-ye@stanford.edu

Jung-Fa TsaiNational Taipei University of Technologyjftsai@cc.kmu.edu.tw

Ming-Hua LinShih Chien Universitymhlin@mail.usc.edu.tw

Yao XieStanford Universityyaoxie@stanford.edu

PP0

Real Case Study - Application of a Memetic Algo-rithm for Scheduling in a Resins Production Plant(Using Parallel Reactors).

As operational changes are often, a memetic algorithm wasdeveloped for production scheduling to adapt to the newsrestrictions (for implemented restrictions). Three differ-ent and parallel reactors depend on the time of productionof each resin and the gradual color increase. The weightfunction prioritizes others important dynamics situations,like v.i.p. customers, raw material prices, etc. The modelwas based on cluster structures population and heuristicsto treat the restrictions.

Ricardo ZibordiElekeiroz S.A. (Ita Industrial Group and Bank)

142 OP08 Abstracts

ricardo.zibordi@elekeiroz.com.br