Conference Program

Index

Welcome from the Chair ............................................ 2Schedule Daily Events & Sessions................................ 3-4Technical Session - Track Schedule.............................. 5-6General Information..................................................... 7Area Map..................................................................... 8School of Economics and Bussiness of Universidad de Chile.................................................... 9-10Events.......................................................................... 11Plenary and Semiplenary Sessions............................... 12-16Technical Sessions........................................................ 17-53Author Index............................................................... 54-58Appendix..................................................................... 59-66 Metro de Santiago Travel & Tour Information PhD in Mathematics, Universidad de Chile Center for Mathematical Modeling, Universidad de Chile

2 Welcome from the Chair

On behalf of the Local Organizing Committee, Program committee and Universidad de Chile, I welcome you to the International Conference on Continuous Optimization ICCOPT 2010. The First ICCOPT was orga-nized in 2004 at Rensselaer Polytechnic Institute (Troy, NY, USA), and the second ICCOPT in 2007 was held in McMaster University (Hamilton, Ontario, Canada). This third version organized for the first in the South Hemisphere will include a Winter School and the four days Conference. I would like to thank Mathematical Optimization Society for hosting ICCOPT 2010 in Chile. It has been an interesting and rewarding challenge for our Optimization community.

The Winter School on Continuous Optimization and Mathematical Modeling will be focus on two subjects: Optimization in natural resources management and Optimization under uncertainty. More than 80 students will attend this school. The Conference will cover most of the areas in Mathematical Optimization and its applica-tions. I expect around 300 participants.

I would like to thank the sponsors: Center for Mathematical Modeling, Faculty of Physical and Mathe-matical Sciences, Faculty of Business and Economics, Universidad de Chile, Millennium Institute Engineering Complex Systems, CONICYT, CNRS and SAS.

Finally, I want to thank all the participants and organizers for coming to Santiago even despite of the strong earthquake in the Chilean Central Region on February 27th. I thank the Program Committee, Plenary speakers, Winter School speakers, session organizers, speakers, students and chairman. I hope you will have during your stay in Santiago fruitful discussions, talks and ideas exchanges. I also hope you will have a chance to visit Santiago’s cultural and neighborhoods attractions.

My best wishes for an interesting and rewarding time in Santiago.

Alejandro JofréChair ICCOPT 2010

Local Organizing Committee

Alejandro Jofré (chair, Universidad de Chile)

Roberto Cominetti (co-chair, Universidad de Chile)

Rafael Correa (co-chair, Universidad de Chile)

Felipe Álvarez (Universidad de Chile)

Jorge Amaya (Universidad de Chile)

Óscar Cornejo (Universidad Católica de la Santísima Concepción)

Fabián Flores-Bazán (Universidad de Concepción)

Pedro Gajardo (Universidad Técnica Federico Santa María)

Fernando Ordóñez (University Southern California, on leave Universidad de Chile)

Héctor Ramírez (Universidad de Chile)

Jorge Rivera (Universidad de Chile)

3

WINTER SCHOOL

Registration: You can pick up your badge, printed program and other materials at the Registration Desk located in the Main Hall of the Conference site.

Opening hours:

Winter School Saturday-Sunday 8:00–17:00 Conference Monday-Thursday 8:00–17:00

SCHEDULE – WINTER SCHOOL

Saturday July 24

9:20–9:30 Welcome address – Alejandro Jofré9:30–11:00 Mathematical models and optimization for mine planning – Felipe Alvarez11:30 11:30 Coffee break11:30–13:00 On optimal and sustainable management of forest plantations – Adriana Piazza13:00–15:00 Lunch15:00–16:30 Viability methods: application to fishery management – Michel de Lara

Sunday July 25

9:00–10:00 Models of optimization under uncertainty – Roger Wets10:10–11:10 Theory and methods for two- and multistage problems – Andrzej Ruszczynski11:10–11:30 Coffee break11:30–12:30 Chance-constrained optimization – Darinka Dentcheva12:30–14:00 Lunch14:00–15:00 Statistical inference and stochastic approximation – Alexander Shapiro15:10–16:10 Risk-averse optimization – Andrzej Ruszczynski16:10–16:30 Coffee break16:30–17:30 Robust optimization – Alexander Shapiro

We plan to follow the notation of the recent book:A. Shapiro, D. Dentcheva and A. Ruszczynski Lectures on Stochastic Programming, SIAM 2009.

Schedule Daily Events & Sessions

Course: Optimization in natural resources management

Course: Optimization under Uncertainty

4 Schedule Daily Events & Sessions

Thursday, July 29

9:00–9:50 Plenary: Philippe Toint10:00–10:30 Coffe Break10:30–12:00 Technical Sessions (ThA)12:00–13:30 Lunch13:30–15:00 Technical Sessions (ThB)15:10–16:00 Semi-Plenary: Jorge Nocedal15:10–16:00 Semi-Plenary: Stefan Ulbrich

Registration: Main Hall Monday–Thursday, 8:00–17:00

Exhibits: Main Hall Monday–Wednesday, 8:30–17:00

SCHEDULE – CONFERENCE

Monday, July 26

8:45–9:00 Welcome address – Alejandro Jofré9:00–9:50 Plenary: Ignacio Grossmann10:00–10:30 Coffe Break10:30–12:00 Technical Sessions (MA)12:00–13:30 Lunch13:30–15:00 Technical Sessions (MB) 15:00–15:30 Coffe Break15:30–17:00 Technical Sessions (MC)17:10–18:00 Semi-Plenary: Zhi Quan Luo 17:10–18:00 Semi-Plenary: Darinka Dentcheva

Tuesday, July 27

9:00–9:50 Plenary: Luis N. Vicente10:00–10:30 Coffe Break10:30–12:00 Technical Sessions (TA)12:00–13:30 Lunch13:30–15:00 Technical Sessions (TB)15:00–15:30 Coffe Break15:30–17:00 Technical Sessions (TC) 17:10–18:00 Semi-Plenary: René Henrion17:10–18:00 Semi-Plenary: Mikhail Solodov

Wednesday, July 28

9:00–9:50 Plenary: Roberto Cominetti10:00–10:30 Coffe Break10:30–12:00 Technical Sessions (WA)12:00–13:30 Lunch13:30–15:00 Technical Sessions (WB)15:00–15:30 Coffe Break15:30–17:00 Technical Sessions (WC)17:10–18:00 Semi-Plenary: Marco Locatelli17:10–18:00 Semi-Plenary: Xiaojun Chen

5Technical Session - Track Schedule

Monday

10:30 - 12:00MA01 Nonsmooth Optimization & Variational Analysis I Active Set Methods in Nonsmooth OptimizationMA02 Optimization in Chemical Engineering I Optimization Models for Chemical ProcessesMA03 Linear Programming MethodsMA04 Financial Optimization

13:30 - 15:00MB01 Nonsmooth Optimization & Variational Analysis II Algorithms for Variational Inequalities and Optimization ProblemsMB02 Optimization in Chemical Engineering II Optimization in Chemical Process DesignMB03 Semidefinite ProgrammingMB04 Mathematical Economics I – General Equilibrium 1

15:30 - 17:00 MC01 Geometry and Optimization IMC02 Dynamic OptimizationMC03 Stochastic ProgrammingMC04 Mathematical Economics II – General Equilibrium 2

Tuesday

10:30 - 12:00TA01 Nonsmooth Optimization & Variational Analysis III Proximal and Alternate Projections MethodsTA02 Optimization in Chemical Engineering III MINLP for Chemical Process SystemsTA03 Natural Resources I Optimization in marine resources managementTA04 Data Envelopment Analysis

13:30 - 15:00TB01 Nonsmooth Optimization & Variational Analysis IV Variational Analysis and ApplicationsTB02 Optimization in Chemical Engineering IV Dynamic Optimization in Chemical Process SystemsTB03 Natural Resources II Optimization in harvesting problemsTB04 Mathematical Economics III – Game Theory

15:30 - 17:00TC01 PDE Constrained OptimizationTC02 Nonlinear Programming Algorithms ITC03 Natural Resources III Optimization of waste management and bioprocessesTC04 Mathematical Economics IV – Contract Theory

6

Wednesday

10:30 - 12:00WA01 Mathematical Models for Data Mining and Game TheoryWA02 Derivative Free Optimization – AlgorithmsWA03 Electricity Portfolio ManagementWA04 Multiobjective optimization

13:30 - 15:00WB01 Linear, Semidefinite and Cone OptimizationWB02 Derivative Free Optimization – ApplicationsWB03 Engineering Optimization IWB04 Global Optimization

15:30 - 17:00 WC01 Geometry and Optimization IIWC02 Nonlinear Programming Algorithms IIWC03 Engineering Optimization IIWC04 Nonsmooth Optimization

Thursday

10:30 - 12:00ThA01 Algorithms for Convex OptimizationThA02 Nonlinear Programming Algorithms IIIThA03 Engineering Optimization IIIThA04 Vector Optimization with Applications I

13:30 - 15:00ThB01 Convex and Nonsmooth AnalysisThB03 Engineering Optimization IVThB04 Vector Optimization with Applications II

Technical Session - Track Schedule

7General Information

Registration and Badges

ICCOPT badges must be worn at all sessions and events. All attendees, including speakers and session chairs, must regis-ter and pay the registration fee. Attendees without badges will be asked to register at the Registration Desk located in the Main Hall. Your registration fee includes the complete technical program and most special programs including the Monday evening reception at 18:30 in the Main Hall, lunch during the School and Conference, all morning and after-noon coffee breaks, and one year individual membership to Mathematical Programming Society. Coffee breaks and lun-ches will be served at the conference site. The Wednesday evening banquet requires a separate payment of US$ 60.

Speaker Guidelines

Audio-Visual ServicesEach session room is equipped with computer and beam projector. We recommend that you put your presentation on a USB stick and arrive at your session 15 minutes in advance to test the connection to the projector before the session starts.If you need to use your own laptop, do not forget to bring a power adaptor. We recommend that you do not attempt to run the presentation off the laptop battery. If your laptop is not compatible with AC power, please bring a suitable electrical adaptor so that you can safely connect to Chilean electricity (220V/50Hz). If your laptop is a Mac, you will further need the appropriate video output adapter.

Presentation GuidelinesThe code for the session on which your presentation has been scheduled can be found in the Author Index at the end of this booklet. The room and location of your session are listed in the Technical Session section of this program. We recommend that you arrive at your session 15 minutes in advance for AV setup and to check with the session chair. Time your presentation to fit within your designated time span, leaving 5 minutes for audience questions.

Program Information DeskIf you have questions about the meeting and/or about your own presentation, stop at the Program Information Desk lo-cated in the Main Hall. We ask the session chairs to notify the Information Desk about any last minute changes or cancella-tions; these changes will be posted outside the session rooms.

Assistant MonitorsShould you experience any problems in your session related to AV needs or any other requests, please go the Registra-tion Desk in the Main Hall and ask for an Assistant Moni-tor.

Session Chair Guidelines

Please check on the Author Index whether you have been designated to chair one or more sessions. In this case, the corresponding session code is the one printed within paren-thesis next to your name. The role of the Chair is to intro-duce each speaker and to coordinate the smooth running of the session. We particularly ask you to make sure that the session begins and ends on time. Each session lasts 90 minu-tes, with equal time allocated to each speaker.

Internet Access

Free wireless access is available in the main building (user-name: iccopt2010 / password: iccopt2010). Alternatively, in-ternet access is also available on the computer rooms H001, H002, H003. These rooms are open Monday-Thursday 9:00-17:00.

Conference Banquet Tickets

The Wednesday evening banquet is open to attendees and guests who paid in advance for tickets. The tickets should be included in your registration envelope. There may be a limited number of tickets available on site. Go to the Regis-tration Desk to inquire. The cost of each ticket is US$ 60.

Messages

The best way for people to reach you is to contact you di-rectly at your hotel. Please leave your hotel phone number with your colleagues and family members. For urgent messa-ges call the Registration Desk +56 2 9783951. Registration staff will transcribe the message and post it on the message board located near the registration. Please check the board periodically to see if you have any messages.

Meeting Rooms

Meeting rooms are available on the second floor: H201–H204.

8 Area Map

The talks will be held in the Tecnoaulas Building at the School of Economics and Bussiness of Universidad de Chile, located on Diagonal Paraguay 257 in the Downtown area of Santiago, within 5 minute walk across a nice small park from the closest subway station (Universidad Católica) and public transportation.

9School of Economics and Bussiness of Universidad de Chile

006 005 004

Toilets

computer rooms

AuditoriumPricewaterhouseCoopers

Floor -1

Floor 1

104Toilets

Casino Co�e & Lunch

AulaMagna

SALAMultiuso

103 102

Accreditations

10 School of Economics and Bussiness of Universidad de Chile

The Faculty of Economics and Business of Universidad de Chile is located near to the city center (Diagonal Pa-raguay 257) could be accessed by subway line Nº 1 (red line), Universidad Católica Station.

203Toilets 202 201204

205

Floor 2

The Faculty

11Events

Welcome Cocktail

The Welcome Cocktail will be held in the Faculty of Economics and Business of the Universidad de Chile. Address: Diagonal Paraguay Street 257, Santiago, at 18:30 pm - July 26, 2010

The Official Dinner

The Official Dinner will take place on Thursday, July 29 at 20:30 hours, in the Castillo Hidalgo, (Castle Hidalgo), located in Santa Lucia 299 at the top of the Cerro Santa Lucia.

If you need aditional information please do not hesitate to contact our Organizing Committee, we will be glad to help you.

Castillo Hidalgo, (Castle Hidalgo), located in Santa Lucia 299 at the top of the Cerro Santa Lucia.

Plenary and Semiplenary Sessions

PLENARY & SEMI-PLENARY SESSIONS — MONDAY 13

� MP – PLENARYMonday, 9:00–9:50 / Aula MagnaChair: Alejandro Jofre

The role of relaxations in linear andnonlinear generalized disjunctive pro-gramming problems

Ignacio GrossmannCarnegie Mellon University / USA

Generalized disjunctive programming (GDP) is anextension of the well-known disjunctive programmingparadigm developed by Balas. The GDP formulationinvolves Boolean and continuous variables that arespecified in algebraic constraints, disjunctions andlogic propositions, which is an alternative represen-tation to the traditional mixed integer programming(MIP) formulation. This class of problems, which hasbeen motivated by its potential for improved model-ing and solution methods, has led to the developmentof customized algorithms that exploit the underlyinglogical structure of the problem in both the linear andnonlinear cases. However, an outstanding questionthat has remained is the exact relationship betweenGDP and disjunctive programming. We establish forthe linear case connections between disjunctive pro-gramming with continuous variables and generalizeddisjunctive programming. Based on these connec-tions we propose a novel family of MIP reformula-tions corresponding to the original GDP model thatresult in tighter continuous relaxations that subsumethe well known big-M and hull relaxations. We ex-tend this analysis to nonlinear GDP problems, wherewe describe the application of these ideas to the op-timization of bilinear and concave GDP problems inwhich continuous relaxations that yield tight lowerbounds are key to the effectiveness of global opti-mization algorithms.

� MSP1 – SEMI-PLENARYMonday, 17:10–18:00 / Rooms H004 & H005Chair: Tamas Terlaki

Optimization methods for spectrummanagement

Zhi Quan LuoUniversity of Minnesota / USA

Consider a communication system whereby multi-ple users share a common frequency band and mustchoose their transmit power spectra jointly in re-sponse to physical channel conditions including the

effects of interference. The goal of the users is to max-imize a system-wide utility function (e.g., weightedsum-rate of all users), subject to individual powerconstraints. A popular approach to solve the dis-cretized version of this nonconvex problem is by La-grangian dual relaxation. Unfortunately the dis-cretized spectrum management problem is NP-hardand its Lagrangian dual is in general not equivalentto the primal formulation due to a positive dual-ity gap. In this work, we use a convexity result ofLyapunov to estimate the size of duality gap for thediscretized spectrum management problem and showthat the duality gap vanishes asymptotically at therate O(1/

√N), where N is the size of the uniform

discretization of the shared spectrum. If the channelsare frequency flat, the duality gap estimate improvesto O(1/N). Moreover, when restricted to the FDMAspectrum sharing strategies, we show that the La-grangian dual relaxation, combined with a linear pro-gramming scheme, can generate an ε-optimal solutionfor the continuous formulation of the spectrum man-agement problem in polynomial time for any ε > 0.

� MSP2 – SEMI-PLENARYMonday, 17:10–18:00 / Rooms H006 & H104Chair: Roger Wets

Optimization with stochastic domi-nance constraints

Darinka DentchevaStevens Institute of Technology / USA

Stochastic orders formalize preferences among ran-dom outcomes and are widely used in statistics andeconomics. We focus on new stochastic optimizationmodels involving stochastic dominance relations asconstraints that relate performance functionals, de-pending on our decisions, valued in an appropriateLp-space, to benchmark random outcomes. Neces-sary and sufficient conditions of optimality and dual-ity theory for these problems will be presented. Theanalysis puts additional light on the expected utilitytheory, the dual (rank-dependent) utility theory, andthe theory of coherent measures of risk. The opti-mization models with stochastic ordering constraintsprovide a link between various approaches for risk-averse optimization. Furthermore, the results con-tribute to the theory of semi-infinite and compositeoptimization in vector spaces. Numerical methodsfor solving problems with dominance constraints willbe sketched. Potential applications will be outlined.

14 PLENARY & SEMI-PLENARY SESSIONS — TUESDAY

� TP – PLENARYTuesday, 9:00–9:50 / Aula MagnaChair: Stephen Wright

Direct search and interpolation-basedmethods in limit situations

Luis N. VicenteUniversity of Coimbra / Portugal

Direct search is a popular class of algorithms forthe minimization of a function without derivatives.Most direct-search methods are based on evaluatingthe objective function at a set of (poll) pointsdefined by a positive spanning set. We will studythe behavior of direct-search methods under generaland adverse conditions, (i) looking at its globalconvergence properties and numerical performancewhen the objective function is discontinuous, (ii)presenting a worst case complexity bound on thenumber of function evaluations, (iii) extending themto multiobjective optimization (Direct MultiSearch)by essentially changing the polling paradigm toincorporate nondominancy tests. On the side ofinterpolation-based trust-region methods, we areinterested in extracting as much function informationas possible from as fewer function evaluations aspossible when using interpolation models. We showthat is possible to compute models with the sameaccuracy as second order Taylor models, for func-tions with sparse Hessians, using much less pointsthan the number required for determined quadraticinterpolation, when minimizing the `1-norm of theHessian model coefficients to build the underdeter-mined quadratic models — this result is based onrecent developments in Compressed Sensing andsparse orthogonal expansions. We have successfullytested a practical interpolation-based trust-regionmethod using both the minimum Frobenius and`1-norm quadratic underdetermined models, showingthe ability of the `1 approach to improve the resultsof the Frobenius one in the presence of someform ofsparsity in the Hessian of the objective function.

� TSP1 – SEMI-PLENARYTuesday, 17:10–18:00 / Rooms H004 & H005Chair: Jorge Vera

Optimization problems with proba-bilistic constraints

Rene HenrionWeierstrass Institute Berlin / Germany

Many optimization problems in engineering sciencesare affected by uncertain parameters. Probabilisticconstraints (PCs) provide an important tool formodeling such problems. As compared to theconventional deterministic case, the presence of arandom variable creates new challenges in theoryand numerics. The talk presents some basic modelsof linear PCs, illustrates their potential applications,collects some principal structural properties of suchconstraints, discusses a specific numerical approachand finally briefly touches aspects of stability.Numerical results are illustrated for an applicationin hydro power management.

� TSP2 – SEMI-PLENARYTuesday, 17:10–18:00 / Rooms H006 & H104Chair: Jonathan Eckstein

Sharp local convergence analysis ofNewtonian methods for constrained op-timization

Mikhail SolodovInstituto de Matematica Pura e Aplicada / Brazil

In this talk, we shall discuss some recent ad-vances in convergence analysis of several primal-dualNewton-type methods for optimization. These in-clude several variants of the sequential quadratic pro-gramming algorithm (quasi-Newton, truncated, sta-bilized), the linearly constrained (augmented) La-grangian method, and some others. A perturbedJosephy-Newton framework and a perturbed SQPframework are introduced, which allow to treat thealgorithms in question in a unified way, dispensingwith some of the previous commonly used assump-tions (such as strict complementarity and linear in-dependence of gradients of active constraints). Forstabilized SQP, by a different Newtonian analysis weobtain superlinear convergence under second-ordersufficient condition without any assumptions on theconstraints at all (i.e., no constraint qualifications).Moreover, rather surprisingly, the same Newtonianline of analysis applies to the augmented Lagrangianalgorithm (method of multipliers), which is, in prin-ciple, not a Newton-type method. Finally, scenariosof dual behavior of the methods in question are dis-cussed in the case when Lagrange multipliers are notunique, and the role of special (critical) multipliers ishighlighted.

PLENARY & SEMI-PLENARY SESSIONS — WEDNESDAY 15

� WP – PLENARYWednesday, 9:00–9:50 / Aula MagnaChair: Alexander Shapiro

Equilibrium and learning in trafficnetwork games

Roberto CominettiUniversidad de Chile / Chile

Congestion is a common characteristic in moderntelecommunication networks as well as in transporta-tion systems of large urban areas. In this talk wereview some recent developments in modeling trafficequilibrium in congested networks. Starting fromthe classical models of Wardrop Equilibrium andStochastic User Equilibrium, we will present in moredetail the notion of Markovian Traffic Equilibriumas well as numerical methods for computing it. Wewill show how all these equilibrium models admit aunified reformulation in terms of a strictly convexmathematical program. From these static equilib-rium notions we move on to present a recent attemptto model the dynamic behavior of travelers by usinga stochastic adaptive-learning process, and describeits asymptotic convergence towards equilibrium.

� WSP1 – SEMI-PLENARYWednesday, 17:10–18:00 / Rooms H004 & H005Chair: Fabian Flores-Bazan

On convex envelopes and underestima-tors for bivariate functions

Marco LocatelliUniversita di Parma / Italy

Convex underestimators of a nonconvex functionf over some region X are very important in thedevelopment of branch-and-bound techniques for thesolution of global optimization problems. The best(largest) possible of such underestimators is calledconvex envelope of f over X. Unfortunately, thederivation of the convex envelope is not a simpletask. All the same some results exist for simple do-mains and/or low-dimensional functions. In this talkwe will discuss convex underestimators for bivariatefunctions. We will first present a method for derivingconvex envelopes over the simplest two-dimensionalpolytopes, i.e., triangles. Next, we propose atechnique to compute the value at some point ofthe convex envelope over a general two-dimensionalpolytope, together with a supporting hyperplane of

the convex envelope at that point. Noting that theenvelopes might be of quite complicated form andtheir computation not easy, we will move later on tothe discussion of a method, based on the solution ofa semidefinite program, to derive convex underesti-mators (not necessarily convex envelopes) of simpleenough form for bivariate quadratic functions overgeneral two-dimensional polytopes.

� WSP2 – SEMI-PLENARYWednesday, 17:10–18:00 / Rooms H006 & H104Chair: Rafael Correa

Nonsmooth, nonconvex minimizationproblems with applications

Xiaojun ChenThe Hong Kong Polytechnic University / Hong Kong

This talk will discuss nonsmooth, nonconvex opti-mization problems in stochastic equilibrium prob-lems, l2-lp (0 < p < 1) minimization problems anddistribution of points on the sphere, as well as theirapplications in transportation planning, signal recon-struction and variable selection. In particular, thistalk will present our recent results in the followingtwo parts.

(i) We reformulate the stochastic variational in-equality problems as expected residual mini-mization problems using residual functions ofvariational inequalities. Mathematical theoremsand practical examples of traffic assignmentsshow that the reformulations are robust and re-liable in uncertain environments.

(ii) We derive a lower bound theory for nonzero en-tries in every local minimizer of the l2-lp min-imization problems. This theory shows clearlythe relationship between the sparsity of the so-lution and the choice of parameters in the model.We prove global convergence of the l1 reweightedminimization algorithm and uniqueness of so-lution under the truncated null space propertywhich is weaker than the restricted isometryproperty.

16 PLENARY & SEMI-PLENARY SESSIONS — THURSDAY

� ThP – PLENARYThursday, 9:00–9:50 / Aula MagnaChair: Felipe Alvarez

Cubic regularization algorithm andcomplexity issues for nonconvex opti-mization

Philippe TointUniversite de Namur / Belgium

We consider regularization methods for the non-convex unconstrained and convexely constrainedoptimization problems. After motivating these al-gorithms, we review known convergence results andemphasize their remarkable complexity properties,that is the number of function evaluations that areneeded for the algorithm to produce an epsilon-critical point. We also discuss the complexity of thewell-known steepest-descent and Newton’s methodin the unconstrained case and report some surprisingconclusions regarding their relative complexity.

� ThSP1 – SEMI-PLENARYThursday, 15:10–16:00 / Rooms H004 & H005Chair: Fernando Ordonez

A semi-stochastic Newton method andpiecewise linear models for nonlinearoptimization

Jorge NocedalNorthwestern University / USA

This talk presents two contributions in nonlinear pro-gramming. The first concerns a new class of methodsfor machine learning and stochastic programmingthat we call “semi-stochastic”. The key observationis that one can design practical Newton-like methodsfor problems involving millions of variables andtraining points by incorporating sampled secondorder information through Hessian-vector products.We demonstrate the efficiency of the new methodson a production-level speech recognition problemprovided by Google.In the second part of the talk, the emphasis ison general purpose methods for large scale opti-mization. We propose an algorithm in which theactive-set prediction phase employs a piecewise linearapproximation to the Hessian of the Lagrangian.The algorithm scales up well in the number ofvariables (unlike sequential quadratic programmingmethods) and is more effective than methods that

base the active-set prediction on sequential linearprogramming.

� ThSP2 – SEMI-PLENARYThursday, 15:10–16:00 / Rooms H006 & H104Chair: Frederic Bonnans

Adaptive multilevel techniques forPDE-constrained optimization

Stefan UlbrichTechnische Universitat Darmstadt / Germany

In the context of PDE-constrained optimizationthe appropriate interplay of optimization methodswith error estimation and adaptive discretizationsoffers the potential for a significant improvementin efficiency, since most optimization iterations canbe carried out on relatively coarse discretizationsand the progress of the optimization process isensured by appropriate mesh refinement. Moreover,the generated hierarchy of discretizations can beused to apply multilevel techniques for the solutionof subproblems. In this talk we describe recentdevelopments in adaptive multilevel optimizationmethods by using appropriate residual based errorestimators or, alternatively, goal-oriented error esti-mators. Here, we consider optimization problems forstationary as well as instationary PDEs. Moreover,we illustrate for several examples how the multilevelhierarchy can be used to construct preconditionersand fast iterative solvers for the arising subproblems.We illustrate the apporaches by several numericalexamples.

Technical Sessions

18 TECHNICAL SESSIONS — MONDAY

MONDAY

� MA01Room H004 - Monday 10:30–12:00ClusterNonsmooth Optimization & Variational AnalysisOrganizers: C. Sagastizabal, W. Hare

Active Set Methods in Nons-mooth OptimizationInvited sessionOrganizer/Chair: Warren Hare

1. Algorithms and identification fornonsmooth optimization

Stephen Wright, University of Wisconsin, 1210 W

Dayton Street, Madison, Wisconsin, 53706, USA,

swright@cs.wisc.edu / Co-author: Adrian Lewis

In constrained optimization, effective identificationof the constraints that are active at the solutioncan speed the asymptotic convergence and improverobustness of algorithms. We discuss an extension ofidentification to composite nonsmooth minimizationinvolving a prox-regular function, showing in par-ticular that optimal manifolds that satisfy a partialsmoothness condition can be identified by solving aregularized linearized subproblem. We outline theproperties of an algorithm based on this subproblem,showing that asymptotic superlinear convergencecan be achieved under certain assumptions.

2. Identifying active manifolds usingproximal points and/or regularization

Warren Hare, University of British Columbia, Okana-

gan Campus, Mathematics, 3333 University Way,

Kelowna, BC, V1V 1V7, Canada, warren.hare@ubc.ca

The minimization of an objective function over aconstraint set can often be simplified if the activemanifold of the constraints set can be correctlyidentified. In this work we present a simple subprob-lem, which can be used inside of any (convergent)optimization algorithm, that will identify the activemanifold of a prox-regular partly smooth constraintset in a finite number of iterations. That is, aftera finite number of iterations, all future iterates willlie on the active manifold. We then examine thel1-regularization method of Tseng and Yun (2009).We reexamine Tseng and Yun’s algorithm in terms ofactive set identification, showing that their method

will correctly identify the active manifold in a finitenumber of iterations. This confirms a conjectureof Tseng that a given class of local approximationscorrectly identifies the active manifold from anypoint in the neighborhood of a solution.

3. Science fiction in nonsmooth opti-mization

Robert Mifflin, Washington State University, WSU,

Pullman WA 99164-3113, USA, mifflin@math.wsu.edu

In the late 1970’s Lemarechal found that a BFGSquasi-Newton method for smooth optimization per-formed very well on some nonsmooth test functions.Such results were confirmed in 2008 in work by Lewisand Overton where they obtained numerical R-linearconvergence on their nonsmooth test functions.In the 1980’s Lemarechal said that “Superlinearconvergence in nonsmooth optimization is sciencefiction”. However, in the 1990’s he, along withOustry and Sagastizabal, created the U-Lagrangianand U-Hessian, leading to the hope for such rapidconvergence. We discuss the current state of affairsfor such a result in theory and for practice we givea BFGS VU-algorithm that appears to show theachievement of science fiction.

� MA02Room H005 - Monday 10:30–12:00

ClusterOptimization in Chemical EngineeringOrganizers: I. Grossmann, L.T. Biegler

Optimization Models for Chem-ical ProcessesInvited sessionChair: Lorenz T. Biegler

1. A comparison between two ways ofstochastic optimization for a dynamichydrogen consuming plant

Daniel Navia, Universidad de Valladolid, Facultad de

Ciencias, Departamento de Ing. Sistemas y Automatica,

Paseo Prado de la Magdalena s/n, 47011 Valladolid,

Spain, daniel.navia@autom.uva.es / Co-authors: Daniel

Sarabia, Gloria Gutierrez, Cesar de Prada

The following work shows the application of twomethods of stochastic optimization in a hydrogenconsuming plant: Two-stage stochastic program-

TECHNICAL SESSIONS — MONDAY 19

ming and Chance constrained optimization. Thesystem presents two main sources of uncertaintydescribed with a binormal probability distributionfunction (PDF). For calculating the probabilisticconstraints inverse mapping method was used. Onthe other hand, to solve the two stage optimizationa discretization of the PDF in scenarios was appliedin order to overcome the calculus limitations im-posed by continuous PDF, and then a frameworkgeneralizing this solution based in interpolation wasproposed. The outcomes of the optimization testedin Montecarlo simulation shows that the two-stageoptimization with the method of generalizationproposed here presents better performance thanchance constrained formulation in terms of feasibilityand optimality for the hydrogen feeding point.

2. Estimation of domains of attractionof ideal reactor separator networkswith mass recycle

J. Alberto Bandoni, PLAPIQUI (UNS-CONICET),

Camino La Carrindanga km. 7, Bahıa Blanca, Ar-

gentina, abandoni@plapiqui.edu.ar / Co-authors: Luis

G. Matallana, Anıbal M. Blanco

The Domain of Attraction (DOA) of an asymptoti-cally stable equilibrium point of a dynamic systemis the region of the state space where trajectoriesthat converge to such equilibrium originate. DOAsare complicated sets, which do not admit analyticalrepresentation except in special cases. Estimationsof the DOAs are relevant in operation of nonlineardynamic systems and many techniques have beenproposed so far. In particular, the Lyapunov stabil-ity theory, which provides an energetic approach todynamic stability analysis, is the basis of a familyof techniques whose rationale is to approximate theDOA by a level set of a Lyapunov function of thesystem under study. In this contribution the rationalLyapunov functions are applied to the estimationof the domains of attraction of different reactorseparator networks with mass recycle configuration,which is a simplified typical chemical process. Aglobal optimization based approach is used to solvethese problems.

3. Synthesis and design of WWT plantsfor biological nitrogen and phosphorusremoval

Noelia Alasino, FCEFyN-Univ. Nacional de Cordoba,

A. Williams 2675, B Los Naranjos, CP 5010, Cordoba,

Argentina, nalasino@santafe-conicet.gov.ar / Co-authors:

Miguel Mussati, Nicolas Scenna, Pio Aguirre

A superstructure model developed for simultane-ous optimization of the process configuration andequipment dimensions, and the operation conditionsof activated sludge wastewater treatment plants,accounting for phosphorus and nitrogen removalis here presented. The ASM3+Bio-P are used tomodel the reaction compartments, and the Takacsmodel for representing the secondary settler. Theperformance criterion selected is the minimizationof the net present value, while verifying compliancewith the effluent permitted limits. The problemis posed as a NLP problem, specifically a DNLP.The optimization model is implemented and solvedusing GAMS. Optimal configurations and designsobtained for several case studies are reported anddiscussed. A sensitivity analysis of some selectedmodel parameters was made for an optimal solutionobtained. The model itself and the resolutionmethodology prove to be robust and flexible enoughto solve efficiently scenarios with a wide range ofoperation conditions, embedding conventional andnon-conventional process configurations.

� MA03Room H006 - Monday 10:30–12:00

Linear Programming MethodsContributed sessionChair: Jacek Gondzio

1. Linear optimization: complexity,algorithms and conjectures in

Tamas Terlaky, Lehigh University, 200 West Packer

Avenue, Bethlehem, PA 18015USA, terlaky@lehigh.edu

In this talks we briefly review some fundamentalalgorithmic concepts for Linear optimization. Thealgorithms include elimination and pivot algorithms,ellipsoid and interior point methods and the per-ceptron algorithm. Complexity and convergence ofthe algorithms are reviewed. Open problems andconjectures related to both pivot algorithms andinterior point methods are discussed. Finally, weconsider how the various algorithms could utilizereadily available multi-core architectures.

20 TECHNICAL SESSIONS — MONDAY

2. Primal-dual column generationmethod for combinatorial optimizationproblems

Pablo Gonzalez-Brevis, The University of Edinburgh,

24/3 Guthrie Street, Edinburgh, United Kingdom,

P.Gonzalez-Brevis@sms.ed.ac.uk / Co-authors: Jacek

Gondzio, Pedro Munari

Relaxations and decomposition techniques haveproven to be a reliable way to exploit separabilityand to transform difficult large-scale problemsinto related easier subproblems. The ability tobenefit from their similarities is a key requirementfor any successful optimization technique. In thistalk we shall demonstrate how primal-dual columngeneration method (PDCGM) may be applied tosolve relaxations of well-known combinatorial opti-mization problems. Primal-dual column generationapproach is based on the infeasible primal-dualinterior point method (IPM) and therefore offersseveral advantages in this context. In particularIPMs provide natural stabilization technique andremedy any potential degeneracy in the solution of asequence of relaxations making it highly competitiveto the state-of-the-art algorithms usually appliedin this context. Preliminary results of our ongoingresearch will be presented to support the view thatprimal-dual methods can and should be used to solvecombinatorial optimization problems.

3. Limited-memory matrix-free inte-rior point method

Jacek Gondzio, School of Maths, Edinburgh Uni-

versity, Edinburgh, EH9 3JZ, United Kingdom,

J.Gondzio@ed.ac.uk

A redesign of Interior Point Methods (IPMs) forLP/QP problems will be addressed. It has twoobjectives: (a) to avoid an explicit access to theproblem data and to allow only matrix-vectorproducts to be executed with the Hessian andJacobian and its transpose; and (b) to allow themethod work in a limited-memory regime. Thenew approach relies on the use of iterative methodswith a specially designed preconditioner to solve thereduced Newton systems arising in optimization withIPMs. Numerical properties of the preconditionerwill be analysed and its use will be illustrated bycomputational results obtained for very large scaleoptimization problems. The ability to work in alimited-memory regime makes the approach particu-

larly attractive when solving problems which are solarge that nothing but storing them is already prob-lematic. A paper related to this talk is available from:http://www.maths.ed.ac.uk/ gondzio/reports/mtxFree.html

� MA04Room H104 - Monday 10:30–12:00

Financial OptimizationContributed sessionChair: Somayeh Moazeni

1. Colombian and U.S stockmarket’sstructural dependence, an aproxima-tion with Copulas

Daiver Cardona, Universidad Autonoma de Occidente,

Cra 103 #11-40 Cali, Colombia, daiver66@gmail.com

In this work, measures of general and tail depen-dence with Copulas were used in order to determi-nate the Colombian and U.S stockmarket’s struc-tural dependence. Losses of Col20, Dow Jonesand Standard&Poors 500 were use as variables.AR(P)-GARH-(q, p) models were used to examinethe marginal distributions of losses. The asym-metrized GED was found the best to fit the perturba-tions. T-Students, Gumbell and Galambos were thebest copulas to fit data. If diversification is measurewith dependence coefficients (Rho Spearman and TaoKendall), then it was found that the Colombian andU.S stock market have a low dependence, accord-ing to CAPM, the systematic risk is low and thepossibilities of diversification are higher. Further-more, the estimated tail dependence coefficients showthat the Colombian and U.S stock market have alow asymptotic dependence, e.g., the probability thatboth stock markets have extreme losses at the sametime is very low.

2. The research of stock index fu-tures margin setting model based onimproved genetic wavelet neural net-work technology

Jia Liu, School of Management and Economics, Beijing

Institute of Technology, Haidian District, Beijing 100081,

P.R.China, liujia3891@163.com / Co-authors: Donghua

Zhu, Xuefeng Wang

Establish stock index futures margin forecastingmodel by using Wavelet Neural Network (WNN)technology. An improved training method for WNN

TECHNICAL SESSIONS — MONDAY 21

is presented. BP method was embedded in the Ge-netic Algorithm (GA) operation in order to resolvethe difficulty of detail searching ability, in the laststep of this method the WNN trained by GA searchesthe optimal solution by using BP method once again.Compared with simple Genetic Wavelet Neural Net-work, this algorithm makes significant improvementsin terms of convergent speed and stability. TakingHong Kong Hang Seng Index Future as the researchobject, and selecting prudent index (PI) and oppor-tunity cost index (OCI) to compare and evaluate theproposed model with traditional methods EWMAmodel and EVT-VaR method. Empirical study re-sult shows that the prudent index of this model isthe highest and the opportunity cost is relatively low,therefore, the model established has a better predic-tion effect.

3. Regularized robust optimization ap-proach for the portfolio optimizationproblem

Somayeh Moazeni, University of Waterloo, Canada,

smoazeni@math.uwaterloo.ca / Co-authors: Thomas F.

Coleman, Yuying Li

Execution cost problem minimizes total cost and riskin the execution of a portfolio of risky assets over afixed number of periods. Execution cost is definedby price impact functions. Robust optimization canbe used to account for the uncertainty in the priceimpact functions due to estimation error. We illus-trate that this approach may be unstable with respectto small perturbations in the uncertainty set specifi-cation. We propose a regularized robust optimiza-tion approach for the portfolio execution cost prob-lem. The proposed method is more stable than thetraditional robust optimization. Given any parame-ter specification of the uncertainty set for the impactfunctions, we construct a regularized uncertainty setusing a regularization constraint. This regularizationconstraint is a matrix inequality of the Hessian ofthe objective function and a regularization parame-ter. The solution from our proposed regularized ro-bust optimization is not only robust to the potentialestimation errors in the parameters of the price im-pact functions, but also robust to possible changesin the uncertainty set. The regularization parametercontrols rate of liquidation as well as the degree ofconservatism of the obtained objective value.

� MB01Room H004 - Monday 13:30–15:00ClusterNonsmooth Optimization & Variational AnalysisOrganizers: C. Sagastizabal, W. Hare

Algorithms for Variational In-equalities and OptimizationProblemsInvited sessionOrganizer/Chair: Angelia Nedich

1. Analysis of first order methods forlarge scale optimization

Zhi Quan Luo, University of Minnesota, Department

of Electrical and Computer Engineering, Minneapolis

MN 55455, USA, luozq@ece.emn.edu

In this talk, we review the contributions of PaulTseng on the first order methods for large scalesmooth/nonsmooth optimization, and their impactto contemporary applications such as compressedsensing and image processing.

2. On the complexity of the hybridproximal extragradient method for theiterates and the ergodic mean

Renato Monteiro, School of ISyE, Georgia Tech, At-

lanta, GA 30332, USA, renato.monteiro@isye.gatech.edu

We analyze the iteration-complexity of the hybridproximal extragradient (HPE) method for finding azero of a maximal monotone operator recently pro-posed by Solodov and Svaiter. One of the key pointsof our analysis is the use of new termination criteriabased on the ε-enlargement of a maximal monotoneoperator. The advantage of using these terminationcriteria is that their definition do not depend onthe boundedness of the domain of the operator.We then show that Korpelevich’s extragradientmethod for solving monotone variational inequalitiesfalls in the framework of the HPE method. As aconsequence, using the complexity analysis of theHPE method, we obtain new complexity bounds forKorpelevich’s extragradient method which do notrequire the feasible set to be bounded, as assumedin a recent paper by Nemirovski. Another feature ofour analysis it that the derived iteration-complexitybounds are proportional to the distance of the initialpoint to the solution set. The HPE framework is alsoused to obtain the first iteration-complexity result

22 TECHNICAL SESSIONS — MONDAY

for Tseng’s modified forward-backward splittingmethod for finding a zero of the sum of a monotoneLipschitz continuous map with an arbitrary maximalmonotone operator whose resolvent is assumed tobe easily computable. Using also the frameworkof the HPE method, we study the complexity of avariant of a Newton-type extragradient algorithmproposed by Solodov and Svaiter for finding a zeroof a smooth monotone function with Lipschitzcontinuous Jacobian.

3. Randomized projection algorithmsfor convex minimization

Angelia Nedich, University of Illinois, 117 Transporta-

tion Building, USA, angelia@illinois.edu

This talk is on random projections for constrainedconvex minimization problems, where the constraintset is specified as the intersection of finitely many“simple” constraints. The proposed algorithmsare applicable to the situation where the wholeconstraint set of the problem is not known inadvance, but it is rather learned in time throughobservations. We discuss the proposed algorithmsfor the case when the projection on the individualconstraints is available in a closed form. We alsoconsider the modification of the algorithms to dealwith the case when each individual constraint isgiven by a convex inequality. The behavior of thealgorithms is investigated both for diminishing andnon-diminishing stepsize values.

� MB02Room H005 - Monday 13:30–15:00

ClusterOptimization in Chemical EngineeringOrganizers: I. Grossmann, L.T. Biegler

Optimization in Chemical Pro-cess DesignInvited sessionChair: Ignacio Grossmann

1. Optimization of biotechnologi-cal processes through a combinedoptimization-simulation approach

Jose Ricardo Perez-Correa, P. Universidad Catolica

de Chile, Vicuna Mackenna 4860, Santiago, Chile,

perez@ing.puc.cl / Co-authors: G. Guillen-Gosalbez,

Robert Brunet, Jose A. Caballero, Laureano Jimenez

Here, we combine a widely used simulation packageand optimization tools to develop a new method fordesigning biotechnological processing plants. This isformulated as a mixed-integer dynamic optimization(MIDO) problem solved by a reduced-space decom-position method that iterates between primal andmaster sub-problems. The primal level entails thesolution of a dynamic nonlinear programming sub-problem in which integer decisions, mainly the typeand number of equipments in parallel, are fixed. Thisprimal problem is solved by integrating the processsimulator with an external optimization package.On the other hand, the master level is a tailor madeheuristic that does not rely on any mixed-integerlinear programming (MILP) formulation; therefore,reducing the effect of the non-convexities of themodel. Both levels of the algorithm are solvediteratively until a termination criterion is reached.The application of this methodology to a typical fer-mentation process resulted in an improved economicperformance.

2. Optimization of CO2 capture pro-cess using an aqueous MEA solution

Patricia Mores, CAIMI, UTN-FRRo, Escurra 2879,

Funes, Santa Fe, Argentina, patricia.mores@gmail.com /

Co-authors: Nicolas Scenna, Sergio Mussati

This paper presents a NLP mathematical model tooptimize the operating conditions of the chemicalabsorption process to CO2 removal using MEAaqueous solution. The optimization design problemis to maximize the CO2 absorption efficiency toreach desired CO2 reduction targets. The entirepost-combustion CO2 process is modeled in detail.Temperature, composition and flow-rate profilesof the aqueous solution and gas streams along theabsorber and regenerator, condenser and reboilerheat duties for amine regeneration are considered asoptimization variables. Dimensions of the absorberand regenerator columns as well as the CO2 compo-sition in flue gas are treated as model parameters.GAMS (General Algebraic Modeling System) andCONOPT are used, respectively, to implement andto solve the resulting mathematical model. Theproposed model can not only be used as optimizerbut also as a simulator. Detailed discussion of resultsis presented through different case studies.

TECHNICAL SESSIONS — MONDAY 23

3. Strategy for optimization of CCGTpower plants by solving a simple non-linear equations system and constraintequations

Ezequiel Godoy, CAIMI - FRRo - UTN, Zeballos 1346,

Rosario, Santa Fe, Argentina, ezgodoy@frro.utn.edu.ar /

Co-authors: Sonia Benz, Nicolas Scenna

A strategy for the solution of the optimization prob-lem of minimum cost of combined cycle gas turbinepower plants is presented. Specific relationships,valid at the optimal solution, among selected decisionvariables are used to introduce new constraints tothe optimization problem. Then, the feasible regionis reduced to a “single point”, and the resolutionstrategy becomes equivalent to solving the resultantset of non-linear equations system and constraintequations so achieved to optimize the system. Thisapproach can also be used to achieve reduced modelsfor real time optimization problems.

� MB03Room H006 - Monday 13:30–15:00

Semidefinite ProgrammingContributed sessionChair: Mituhiro Fukuda

1. SDP relaxation for polynomial opti-mization problems and facial reductionalgorithm

Hayato Waki, The University of Electro-

Communications, Choufu-gaoka 1-5-1, Choufu-shi,

Tokyo, Japan, waki@cs.uec.ac.jp / Co-author: Masakazu

Muramatsu

In this talk, we give an SDP problem obtained byLasserre’s SDP relaxation for a one-dimensionalpolynomial optimization problem (POP). The stan-dard SDP solvers, such as SeDuMi and SDPA, returnthe significantly wrong value as the optimal value ofthe SDP problem, but the returned value is equalto the optimal value of the POP. One of reasons forthis strange result is that the SDP problem is verysensitive to the numerical errors in computation ofthe interior-point methods. Moreover, we show thatFacial Reduction Algorithm (FRA) proposed byBorwein and Wolkowicz works for the SDP problemeffectively. In general, FRA generates an SDP withan interior feasible solution from a given SDP. Inour case, we obtain a simple linear programming

problem by applying FRA into the SDP relaxationproblem and find the correct optimal value.

2. Local convergence for sequentialsemidefinite programming

Rodrigo Garces, Universidad de la Frontera, Temuco,

Chile, r.garces02@ufromail.cl / Co-authors: Walter

Gomez, Florian Jarre

We examine the local convergence of the sequentialsemidefinite programming algorithm for solving op-timization problems with nonlinear semidefinitenessconstraints. The papers [1,2] present a proof of localquadratic convergence of this algorithm under theassumption of certain second order sufficient condi-tion for a local minimizer. The present work changesthe analysis of [1] to a weaker second order sufficientcondition and obtains the same convergence result.

[1] B. Fares, D. Noll and P. Apkarian (2002): Robust

control via sequential semidefinite programming. SIAM

J. Control Optim. 40, 1791-1820.

[2] R.W. Freund, F. Jarre and Vogelbusch (2007):

Nonlinear semidefinite programming: sensitivity, con-

vergence, and an application in passive reduced-order

modelling. Math Programming, 109(2-3):581-611.

3. Solving large-scale semidefiniteprograms from quantum chemistry

Mituhiro Fukuda, Tokyo Institute of Technology,

2-12-1-W8-41 Oh-okayama, Meguro-ku, Tokyo 152-8552,

Japan, mituhiro@is.titech.ac.jp / Co-authors: Maho

Nakata, Katsuki Fujisawa

The electronic structure calculation is one of the fun-damental problems in quantum chemistry. Using thenon-traditional reduced density matrix formulationof the problem, we obtain an extremely large-scalesemidefinite program. The advantage of this for-mulation is that it is a more elegant approximationof the original problem in terms of its physical andchemical properties. We recently made a majorupdate in our parallel semidefinite program solverSDPARA 7 which allow us to solve much largerproblems in a shorter time using a cluster computeror a super computer with multi-core CPUs. Wewill report these recently innovations we made inthe solver, and some numerical results on extremelylarge-scale semidefinite programs.

24 TECHNICAL SESSIONS — MONDAY

� MB04Room H104 - Monday 13:30–15:00

ClusterMathematical EconomicsOrganizers: J.M. Bonnisseau, J. Rivera

General Equilibrium IContributed & Invited sessionChair: Carlos Herves

1. Existence of equilibria in economieswith externalities and increasing re-turns in an infinite dimensional space

Matıas Fuentes, Universidad Nacional de San Martın,

Caseros 2241, Z.C. 1650, Buenos Aires, Argentina,

matias.fuentes@unsam.edu.ar

In this paper we consider a general equilibriummodel with an infinite dimensional commodityspace, with externalities affecting to the consumerand producer sets and the preferences relations. Allof these sets are represented by correspondences aswell as the behavior of producers. These conceptswere used in economic theory by Bonnisseau (1997)but we extend the results by considering the spaceof measurable functions essentially bounded. AlsoBonnisseau-Meddeb (1999) use this space. In ourcase, however, we also consider externalities. Forour model we apply the limiting technique used byBewley (1972) but there are four major problemsthat do not permit a direct application of that.To overcome two of these difficulties we proposea strong lower hemi-continuity assumption on theconsumers and producers correspondences. The restof problems are removed when finite economies arebig enough. As a result, an existence theorem isestablished.

2. Set-valued optimization in welfareeconomics

Bao Truong, Northern Michigan University, 1401

Presque Isle Avenue, USA, btruong@nmu.edu / Co-

author: Boris Mordukhovich

In this talk we consider recent applications of set-valued optimization, a far-going extension of vectoroptimization, to convex and nonconvex modelsof welfare economics with finite-dimensional andinfinite-dimensional commodity spaces. We show, inparticular, that the usage of set-valued optimizationallows us to justify the existence of nonlinear prices

in nonconvex models, which support decentralizedconvex-type equilibrium at Pareto optimal alloca-tions, via a common multiplier of a new first-ordernecessary conditions for minimizers to some con-strained set-valued optimization problem. Ourtechniques are mainly based on advanced tools ofvariational analysis and generalized differentiation,in particular, the fundamental extremal principlethat can be treated as a variational counterpart ofthe classical separation in the case of nonconvex sets.

3. Walrasian prices in a market withconsumption rights

Carlos Herves, Universidad de Vigo, Facultad de CC.

Economicas, Campus Unversitario, 36310 Vigo, Spain,

cherves@uvigo.es / Co-authors: Francisco Martınez,

Jorge Rivera

In this paper we consider an exchange economywhere there is an external restriction for the con-sumption of goods. This restriction is defined byboth a cap on consumption of certain commoditiesand the requirement of an amount of rights for theconsumption of these commodities. The caps forconsumption are imposed exogenously due to thenegative effects that the consumption may produce.The consumption rights are distributed among theagents. This fact leads to the possibility of estab-lishing licence or consumption rights markets. Theseconsumption rights do not participate in agents’preferences, however the individual’s budgetary con-straint may be modified, leading to a reassignmentof resources.

� MC01Room H004 - Monday 15:30–17:00

Geometry and Optimization IInvited sessionOrganizer/Chair: Felipe Alvarez

1. Some recent results in Riemannianoptimization

Kyle Gallivan, Florida State University, 1017 Academic

Way, 208 Love Building, Tallhassee FL 32306, USA,

kgallivan@fsu.edu

In this talk I will discuss some recent progress inthe design and analysis of optimization methods onRiemannian manifolds from an ongoing collaborationbetween myself and Anuj Srivastava at Florida State

TECHNICAL SESSIONS — MONDAY 25

University and P.-A. Absil and Paul Van Dooren atthe Catholic University of Louvain. I will presentan overview of our Riemannian Trust Region andRiemannian BFGS optimzation algorithms and amanifold ensemble method for subspace tracking.

2. Recent advances in the Ordejon’sproblem

Paulo J. S. Silva, University of Sao Paulo, Rua do

Matao 1010, Cid. Universitaria, CEP: 05508-090, Sao

Paulo, SP, Brazil, pjssilva@ime.usp.br / Co-author: Jose

M. Martınez

We present recent results on the computation ofelectronic structures based on first principles, specifi-cally on solving Ordejon’s problem. Mathematically,this problem can be stated as the computation ofthe orthogonal projection onto the space spannedby the K eigenvectors associated to the K smallesteigenvalues of a symmetric negative definite matrix.Usually K is a significant fraction of the matrixdimension. We will present optimization techniquesto solve such problem, in particular we will showhow to exploit the sparsity that is present in theproblem data and in the solution. We will also pro-pose a variation of the projected spectral gradientmethod that works remarkably well in this model,being faster than more usual choices as conjugategradients.

3. A variance-expected complianceapproach for topology optimization

Miguel Carrasco, Universidad de los Andes, San

Carlos de Apoquindo 2200, Las condes, Santiago, Chile,

migucarr@uandes.cl / Co-authors: Benjamin Ivorra,

Rodrigo Lecaros, Angel Manuel Ramos

In this talk, we present a stochastic model fortopology optimization based on a previous variance-expected compliance applied to truss design. Theprincipal objective of the variance-expected compli-ance model is to find robust structures for a givenmain load and its random perturbations. In particu-lar, we are interested to avoid high compliance valueswhen a random load is applied. In the first part, werecall the variance-expected formulation, we presentthe main results in the case of truss structures andshow some numerical examples. Then, we presentthe stochastic model in the topology optimizationcase and the main results. Finally, we discuss thismodel using a simple 2D benchmark test case, and

compare the results obtained with those given byan expected compliance model. We obtain robuststructures when loads are randomly perturbed.

� MC02Room H005 - Monday 15:30–17:00

Dynamic OptimizationContributed sessionChair: J. Frederic Bonnans

1. Risk-averse dynamic programmingfor Markov decision processes

Andrzej Ruszczynski, Rutgers University, 94

Rockefelelr Rd, Piscataway, NJ 08854, USA,

rusz@business.rutgers.edu

We discuss methods of dynamic risk measurementand issues of time-consistency. Next, we introducethe concept of a Markov risk measure and we useit to formulate risk-averse control problems for twoMarkov decision models: a finite horizon modeland a discounted infinite horizon model. For bothmodels we derive risk-averse dynamic programmingequations and a value iteration method. For theinfinite horizon problem we also develop a risk-aversepolicy iteration method and we prove its conver-gence. Finally, we propose a version of the Newtonmethod to solve a nonsmooth equation arising inthe policy iteration method and we prove its globalconvergence.

2. Second order analysis in stochasticoptimal control theory

Francisco Silva, INRIA SACLAY, Ecole Polytech-

nique, 59B, Boulevard Jourdan, 75014 Paris, France,

silva@cmap.polytechnique.fr / Co-author: Joseph Fred-

eric Bonnans

In the study of stochastic optimal control problemsthere are two main approaches. The first is based isthe dynamic programming principle which leads toa second order Halmilton-Jacobi-Bellman equationsatisfied by the value function. The second approachconsists in deriving first order necessary optimalityconditions based on a perturbation analysis in thecontrol variable. This leads, in a very general frame-work, to the so-called stochastic maximum principlegeneralizing the standard maximum principle whichis well known in the deterministic framework. Fol-lowing the second approach we derive second order

26 TECHNICAL SESSIONS — MONDAY

necessary conditions for the unconstrained case and,under a polyhedricity assumption, we are able todeal with also with the constrained case. To ourbest knowledge, these are the first results concerningsecond order optimality conditions for the stochasticcase.

3. Second-order conditions for bang-singular extremals

J. Frederic Bonnans, INRIA Saclay & Ecole Polytech-

nique, France, Frederic.Bonnans@inria.fr / Co-authors:

M. Soledad Aronna, Andrei Dmitruk, Pablo Lotito

We consider an optimal control problem whoseHamiltonian function is affine w.r.t. the (vector)control variable. The initial and final states areconstrained by a finite number of equalities andinequalities, and the control has to be nonnegative.Extending the Goh transformation technique to thissetting, we are able to derive second-order necessaryconditions expressed in terms of the transformedcritical directions. Under a certain decouplingassumption (always satisfied in the case of a scalarcontrol), we obtain a characterization of quadraticgrowth. The results will be published in an INRIAResearch Report, to appear.

� MC03Room H006 - Monday 15:30–17:00

Stochastic ProgrammingContributed sessionChair: Sergio Bruno

1. An introduction to stochasticsemidefinite programs

Baha Alzalg, Washington State University, 1615 SE

Bleasner Dr. Apt. 47, Pullman, WA 99163, USA,

baha2math@gmail.com

Semidefinite programs (SDPs) are a class of convexoptimization problems. In SDPs we minimize alinear objective function over symmetric positivesemidefinite matrix variables with linear constraints.Linear programs (LPs) are a special case of SDPs.SDPs have generated interest because SDP algo-rithms allow the solution of problems previouslyunsolvable by the techniques convex optimization.Both LPs and SDPs are defined using deterministicdata. Stochastic programs (SPs) are a way of dealingwith uncertain data in LPs and produce solutions

that minimize the expected performance. A naturalquestion that arises is whether there is an extensionof SDPs to deal with uncertainty in data the way SPsdo for LPs. Recently, Ariyawansa and Zhu (2006)have answered this question affirmatively by definingStochastic Semidefinite Programs (SSDPs). In mypresentation I will introduce SSDPs as a paradigmfor dealing with uncertainty in data defining SDPs.

2. SDDP for stochastic programs basedon extended polyhedral risk measures

Vincent Guigues, PUC-Rio, Rua Marques de

Sao Vicente, 225, Gavea - Rio de Janeiro, Brazil,

vguigues@puc-rio.br / Co-author: Werner Romisch

We define a risk averse nonanticipative feasible pol-icy for multistage stochastic programs and proposea methodology to implement it. The approach isbased on dynamic programming equations writtenfor a risk averse formulation of the problem. Thisformulation relies on a new class of multiperiod riskfunctionals called extended polyhedral risk measures.Dual representations of such risk functionals aregiven and used to derive conditions of coherence. Inthe one-period case, conditions for convexity andconsistency with second order stochastic dominanceare also provided. The risk averse dynamic program-ming equations are specialized considering convexcombinations of one-period extended polyhedralrisk measures such as spectral risk measures. Toimplement the proposed policy, the approximation ofthe risk averse recourse functions for stochastic linearprograms is discussed. In this context, we detaila stochastic dual dynamic programming algorithmwhich converges to the optimal value of the riskaverse problem.

3. Real asset portfolio optimizationusing coherent risk measures

Sergio Bruno, Petrobras, Av. Quintino Bocaiuva,

343 apt 602, Brazil, svbbruno@gmail.com / Co-author:

Claudia Sagastizabal

In this study we consider the case of a companyworking on gas commercialization, particularly inBrazil. The investment on gas pipes is one of themost critical long term decisions of the company.This decision is highly dependent on expected gasdemand and production. A large amount of thedemand comes from thermoelectric plants. SinceBrazil has a hydro dominated power system, thermal

TECHNICAL SESSIONS — MONDAY 27

plants are only dispatched as marginal producers,to complement the hydropower. This makes thegas demand of thermal plants fueled by gas veryuncertain and volatile. We propose a model to maxi-mize the company profit, considering gas acquisitionand delivery, network operation costs, contractualpenalties and investment opportunities. The modelis implemented as a two stage stochastic investmentmodel which hedges risk by means of ConditionalValue at Risk constraints.

� MC04Room H104 - Monday 15:30–17:00

ClusterMathematical EconomicsOrganizers: J.M. Bonnisseau, J. Rivera

General Equilibrium IIInvited sessionChair: Jean-Marc Bonnisseau

1. The concavity assumption on felic-ities and asymptotic dynamics in theRSS model

M. Ali Khan, Johns Hopkins University, akhan@jhu.edu

/ Co-author: Adriana Piazza.

The analysis of the RSS model in mathematicaleconomics involves the study of an infinite-horizonoptimal variational problem in discrete time. Underthe assumption that the objective function is uppersemicontinuous and “supported” at the value ofthe maximally-sustainable level of the consumptiongood, we report a far-reaching generalization ofresults on the equivalence, existence and asymptoticconvergence of optimal trajectories in this model.We identify a “symmetry” condition on the zeroesof a “discrepancy function” underlying the objectivefunction that proves to be necessary and sufficient forthe asymptotic convergence of good programs, andreduces to an equivalent “non-interiority” conditionin the standard case of a concave objective function.

2. Computing equilibrium points inincomplete market: a variational ap-proach

Julio Deride, Universidad de Chile, Chile,

jderide@dim.uchile.cl/ Co-author: Alejandro Jofre,

Roger Wets

In this paper we propose an algorithm for computingan equilibrium point for a two periods incompletemarket model. First, an equilibrium point is char-acterized as a solution of a max-min optimizationproblem in which the excess supply function isrelevant. Second, the max-min problem is solved byintroducing the “augmented Walrasian function” andby using local and global approximation techniqueswith multiple start ups. Third, we prove convergenceof the algorithm proposed. Finally, we give somenumerical examples showing how powerful is thisapproach for solving large scale incomplete marketequilibrium problem in which an important numberof agents, consumption goods and nancial contractsare involved.

3. Discrete Walrasian Exchange Pro-cess

Jean-Marc Bonnisseau, Paris School of Economics,

Universite Paris 1 Pantheon-Sorbonne, France, Jean-

Marc.Bonnisseau@univ-paris1.fr / Co-author: Orntangar

Nguenamadji

In an exchange economy, we provide a discreteexchange process, which is Walrasian since thetrades are given by the equilibrium allocation of thelocal equilibrium. We prove that this process attainsa Pareto optimal allocation after a finite number ofsteps and the local equilibrium price then supportsthe Pareto optimal allocation. Furthermore, alongthe process, the allocation is feasible and the utilityof each consumer is non-decreasing.

28 TECHNICAL SESSIONS — TUESDAY

TUESDAY

� TA01Room H004 - Tuesday 10:30–12:00

ClusterNonsmooth Optimization & Variational AnalysisOrganizers: C. Sagastizabal, W. Hare

Proximal and Alternate Projec-tions MethodsInvited sessionOrganizer/Chair: Felipe Alvarez

1. A practical relative error criterionfor the classic augmented Lagrangian

Jonathan Eckstein, Rutgers University, RUTCOR,

640 Bartholomew Road, Piscataway NJ 08854, USA,

jeckstei@rci.rutgers.edu / Co-author: Paulo J.S. Silva

This talk begins by summarizing some recentcomputational work on implementing augmentedLagrangian methods using a box-constrainedconjugate-gradient-like method to (approximately)solve the subproblems. The combination of fea-tures that worked best in practice, namely theclassic quadratic penalty, no proximal regularizingterm, and a relative error criterion to allow highlyapproximate solution of the subproblems, lacks asatisfying convergence theory, even in the convexcase. Inspired by these results, we attempted toprove global convergence in the convex case for amethod of this type, using some form of relativeerror criterion that can be applied directly to theaugmented Lagrangian gradient. Eventually wesucceeded, but the resulting method involves a novelauxiliary sequence that undergoes an extragradient-like update and is Fejer monotone to the primalsolution set without having to converge to it. Wepresent preliminary computational results for thiscriterion.

2. Diagonal and alternating algorithmsfor constrained variational inequalitiesJuan Peypouquet, Universidad Tecnica Federico

Santa Marıa, Av. Espana 1680, Valparaıso, Chile,

juan.peypouquet@usm.cl / Co-authors: Hedy Attouch,

Marc-Olivier Czarnecki

We study diagonal and alternating algorithmsthat combine either an implicit (resolvent) orexplicit (Eulerian) scheme with a simple exterior

penalization procedure. The resulting sequences ofiterates converge weakly to a solution of the givenconstrained variational inequality. Convergence ofthe averages is granted under minimal assumptions.The methods account for inexact computation ofthe iterates. Finally we discuss on how to applythese methods to best response dynamics with costto change, optimal control problems and domaindecomposition for partial differential equations.

3. Interior proximal algorithm withvariable metric for second-order cone

Julio Lopez, Universidad de Chile, Av. Blanco En-

calada 2120, Santiago, Chile, jclopez@dim.uchile.cl /

Co-authors: Felipe Alvarez, Hector Ramırez

In this work, we propose an inexact interior proximaltype algorithm for solving convex second-ordercone programs. This kind of problems consists ofminimizing a convex function (possibly nonsmooth)over the intersection of an affine lineal manifold withthe Cartesian product of second-order cones. Theproposed algorithm uses a distance variable metric,which is induced by a class of positive definitematrices, and an appropriate choice of regularizationparameter. This choice ensures the well-definednessof the proximal algorithm and forces the iterates tobelong to the interior of the feasible set. Also, undersuitable assumptions, it is proven that each limitpoint of the sequence generated by the algorithmsolves the problem. Finally, we described the Bundlemethod with distance variable metric for solving thiskind of problems with objective function nonsmoothand report several numerical tests.

� TA02Room H005 - Tuesday 10:30–12:00

ClusterOptimization in Chemical EngineeringOrganizers: I. Grossmann, L.T. Biegler

MINLP for Chemical ProcessSystemsInvited sessionChair: Ignacio Grossmann

1. Optimization models for planningand scheduling in the carton boardboxes industry

Aldo Vecchietti, INGAR-CONICET-UTN, Avellaneda

TECHNICAL SESSIONS — TUESDAY 29

3657, Santa Fe (3000), Argentina, aldovec@santafe-

conicet.gov.ar / Co-author: Marıa Analıa Rodrıguez

In this work we are presenting a cutting stockproblem for the carton corrugated board boxesindustry. The formulation considers the planningand scheduling of the corrugator machine whereorders must be combined in cutting patterns. Theobjective function minimizes the trim loss andalso the number of patterns to cut. Due to thehigh problem combinatory, a two step algorithm ischosen for planning and variables aggregation for thescheduling problem in order to execute the problemsin short execution times. Results obtained in theexecution of several examples are shown.

2. Global superstructure optimizationfor the design of integrated processwater networks

Ignacio E. Grossmann, Carnegie Mellon University,

Dept. Chemical Engineering, Pittsburgh, PA 15213,

USA, grossmann@cmu.edu

We propose a general superstructure and a model forthe global optimization for integrated process waternetworks. The superstructure consists of multiplesources of water, water-using processes, wastewatertreatment and pre-treatment operations. Uniquefeatures are that all feasible interconnections areconsidered between them and multiple sources of wa-ter can be used. The proposed model is formulatedas a Nonlinear Programming (NLP) and as a MixedInteger Nonlinear Programming (MINLP) problemfor the case when 0-1 variables are included for thecost of piping and to establish optimal trade-offsbetween cost and network complexity. To effectivelysolve the NLP and MINLP models to global op-timality we propose tight bounds on the variableswhich are expressed as general equations. We alsoincorporate the cut proposed by Karuppiah andGrossmann1 to significantly improve the strengthof the lower bound for the global optimum. Theproposed model is tested on several examples.

3. Global optimization of sizing prob-lem in pipe networks

Arvind Raghunathan, United Technologies Research

Center, 411 Silver Lane, MS 129-15, East Hartford, CT

06118, USA, raghunau@utrc.utc.com

Sizing optimization of pipes in a specified networkhas been a problem of interest for the last 50

years. The problem has usually been formulatedas a non-convex and non-smooth mixed integernonlinear optimization problem. Consequently, mostapproaches proposed to solve this problem do notguarantee convergence to a globally optimal solution.In this talk, we present a novel convex mixed integernonlinear programming formulation for the sizingoptimization and describe an algorithm based onouter-approximations for the efficient solution. Theproof of global optimality only requires that thepressure drop function governing the fluid flow inthe pipes be monotonically increasing in the flows.We also present new insights into the hydrauliccalculation problem in piping networks. We showthe problem of hydraulic calculations can be castas a strictly convex nonlinear program. This resultis central to showing the global optimality of theapproach. We present results from optimizing pipesizes in water distribution networks available fromthe literature.

� TA03Room H006 - Tuesday 10:30–12:00

ClusterNatural ResourcesOrganizers: P. Gajardo, V. Albornoz

Optimization in marine re-sources managementInvited sessionChair: Vıctor Albornoz

1. Sustainable yields for ecosystems

Michel De Lara, CERMICS Ecole des Ponts ParisTech,

6 et 8 avenue Blaise Pascal, 77455 Marne la Vallee Cedex

2, France, delara@cermics.enpc.fr / Co-authors: Eladio

Ocana, Ricardo Oliveros-Ramos, Jorge Tam

We define the notion of sustainable yields forecosystem, with particular emphasis on long-runconsistency between ecological and economic con-flicting objectives. We provide a way to computesustainable yields by means of a viability analysisof generic ecosystem models with harvesting. Weapply our approach to a Lotka–Volterra model ofthe anchovy–hake couple in the Peruvian upwellingecosystem between the years 1971 and 1981. Ouranalysis suggests that, during the anchovy collapse,the fishery could theoretically have been viablymanaged to produce catches above the expected

30 TECHNICAL SESSIONS — TUESDAY

levels while ensuring biological conservation. Controltheory and viability theory methods have allowed usto introduce ecosystem considerations, such as multi-species and multiobjectives, and have contributed tointegrate the long term dynamics, which is generallynot considered in conventional fishery management.

2. Fisheries management and intergen-erational equity

Claudio Pareja, Departamento de Ingenierıa

Matematica, Universidad de Chile, Av. Blanco En-

calada 2120, Santiago, Chile, cpareja@dim.uchile.cl /

Co-authors: Ivar Ekeland, Rashid Sumaila

We adapt the classical Schaefer model of fisheriesmanagement to take into account intergenerationalequity, in the line of Sumaila ([18]) and Sumailaand Walters ([19]). The resulting discount rate thenis non-constant, and the planners preferences aretime inconsistent, so that optimal solutions are notimplementable. In the line of Ekeland and Lazrak([6], [7]) we define Markov subgame perfect equilibriaof the underlying sequential game. We characterizeequilibrium strategies by a simple relation, and wereach a robust conclusion, namely that, to take intoaccount intergenerational equity, the rate of timepreference, δ, should be replace by δ − n, where n isthe rate of growth of the human population.

3. A total allowable catch quota in amultispecies Chilean fishery

Vıctor M. Albornoz, Universidad Tecnica Federico

Santa Marıa, Departamento de Industrias, Av. Santa

Marıa 6400, Santiago, Chile, victor.albornoz@usm.cl /

Co-author: Cristian M. Canales

In this paper we present a nonlinear optimizationmodel as a planning tool in the simultaneousexploitation of common sardine (Strangomerabentincki) and anchovy (Engraulis ringens). InChile, the most important fishing regulation instru-ment is the establishment of global and individualcapture quotas for each regulated resource, whosevalues are based on a total allowable capture quota,incorporated as a decision variable in our model.The proposed decisions must take into account thespecies mixture in their catches and must be basedon the knowledge of the population dynamic behav-ior through aging and spatial mathematical relations.

� TA04Room H104 - Tuesday 10:30–12:00

Data Envelopment AnalysisContributed & Invited sessionChair: Charles Vincent

1. An optimization-based method forimputation

Juan Dıaz, Universidad de Chile, Diagonal Paraguay

257, Santiago, Chile, juadiaz@fen.uchile.cl / Co-author:

Jorge Rivera

This paper proposes an alternative vectorial impu-tation method based on an optimization problem.It looks for neighbors according to a criteria thatbalances similarity among characteristics and bestfit with convex combination of them. We also studyits performance in comparison with other well-known imputation procedures by artificial empiricalexercises using sets of real data. The procedurehere developed takes into account the case wherethe imputed vector has to satisfy a given linearconstraint.

2. Efficiency assessment of banking sec-tor units through chance-constraineddata envelopment analysis

Mukesh Kumar, CENTRUM Catolica, Pontificia Uni-

versidad Catolica, Calle 9/s, Los Alamos de Monterrico,

Santiago de Surco, Lima, Peru, mkumar@pucp.edu.pe /

Co-author: Charles Vincent

It is the general belief that efficiency and/or per-formance become strategic variables in tacklingthe increasing competitive pressure and structuralchanges within banking industry. In this paper wefocus on the efficiency assessment to measure thetechnical efficiency of Indian banks by using chanceconstrained data envelopment analysis (CCDEA)in line with Olesen et al. (1995), which envelopesconfidence region for each DMU to determine itsown level of chance. Among the banks there are fewmajor characteristics of interest to the liberalizationissue: like size and ownership. This paper dealswith the ownership characteristic. The results revealthat (i) there is significant reduction in the efficiencyscore of each bank with the rising in chance level ofconstraint, (ii) there is huge difference in the rankingof some of the banks based on deterministic DEAand CCDEA.

TECHNICAL SESSIONS — TUESDAY 31

3. Sum-of-ratios fractional program-ming approach to efficiency evaluationwith AHP weights

Charles Vincent, CENTRUM Catolica, Pontificia Uni-

versidad Catolica, Jr.Daniel Alomia Robles 125-129, Los

Alamos de Monterrico, Santiago de Surco, Lima, Peru,

vcharles@pucp.edu.pe / Co-author: Mukesh Kumar

Efficiency measurement has been a subject oftremendous interest as organizations have struggledto improve productivity. Data envelopment analysis(DEA) is a methodology that allows, in one way orother, the assignment of efficiency scores to membersof a group of decision-making units, which is anincreasingly popular and widely used managementtool. Conventional DEA models consider that inputsand outputs are continuous/discrete amounts withsingle or multiple objectives of special interest. Oneof the strengths of DEA in the measurement oftechnical efficiency is that it willingly accommo-dates multiple-output multiple-input productiontechnologies. In exploiting so, it assumes that eachof the inputs is used jointly in the production ofeach output. In some applied studies, this canbe undesirable too. The efficiency identificationamong the types of assembled printed circuit boards(PCBs) enabled us to design a new disaggregatedformulation that allows a specific output to be madeindependent of a specific input, while maintainingthe joint production relationship for the otheroutputs and inputs. The present article focuses ona special form of multi-objective DEA wherein eachobjective is viewed as a sort of single-ratio frac-tional programming. Analytical hierarchy process(AHP) methodology has been used to determinethe weight of each fractional objective functionthrough decision makers. The derived efficiencyidentification optimization problem has been viewedas a special class of fractional programming knownas sum-of-ratios fractional programming problem.Reduction technique to reform the special structurealong with solving methodology has been providedwith a numerical example.

� TB01Room H004 - Tuesday 13:30–15:00

ClusterNonsmooth Optimization & Variational AnalysisOrganizers: C. Sagastizabal, W. Hare

Variational Analysis and Appli-cationsInvited sessionOrganizer/Chair: Jiri Outrata

1. Optimality conditions in control ofmonotone variational inequalities

Jiri V. Outrata, Academy of Sciences of the Czech

Republic, Institute of Information Theory and Automa-

tion, Pod Vodarenskou vezi 4, Prague, Czech Republic,

outrata@utia.cas.cz / Co-authors: Jiri Jarusek, Jana

Stara

The contribution concerns optimal control of a classof strongly monotone variational inequalities, whosesolution maps are directionally differentiable. Thisproperty is used to derive sharp pointwise necessaryoptimality conditions, provided we do not imposeany control or state constraints. In presence ofsuch constraints we derive, under a mild constraintqualification, optimality conditions in a “fuzzy”form. For strings, these conditions may serve asan intermediate step toward pointwise conditionsof limiting (Mordukhovich) type and in the caseof membranes they lead to a variant of Clarkestationarity conditions.

2. On topological properties of min-max functions

Vladimir Shikhman, RWTH Aachen, Templergraben

55, Germany / Co-authors: D. Dorsch, H. Th. Jongen

We examine the topological structure of the upper-level set Mmax given by a min-max function ϕ.It is motivated by recent progress in GeneralizedSemi-Infinite Programming (GSIP). We formulatetwo assumptions (Compactness Condition CC andSym-MFCQ) which imply that Mmax is a Lipschitzmanifold (with boundary). The Compactness Con-dition is shown to be stable under C0-perturbationsof the defining functions of ϕ. Sym-MFCQ can beseen as a constraint qualification in terms of Clarke’ssubdifferential of the min-max function ϕ. Moreover,Sym-MFCQ is proven to be generic and stable underC1-perturbations of the defining functions which

32 TECHNICAL SESSIONS — TUESDAY

fulfill the Compactness Condition. Finally we applyour results to GSIP and conclude that genericallythe closure of the GSIP feasible set is a Lipschitzmanifold (with boundary).

3. Computation of pessimistic solu-tions to MPECs

Michal Cervinka, Academy of Sciences of the Czech

Republic, Institute of Information Theory and Automa-

tion, Pod Vodarenskou vezi 4, cervinka@utia.cas.cz /

Co-authors: Ctirad Matonoha, Jiri V. Outrata

We present a new numerical method to compute theso-called relaxed pessimistic solutions to mathemati-cal programs with equilibrium constraints (MPECs)where the solution map arising in the equilibriumconstraint is generally not single-valued. Thismethod combines two existing codes: BOBYQA forderivative-free optimization under box-constraints,and a variant of the Newton method for solvingMPECs from the interactive system UFO. Wecomment on post-optimization analysis and reporton numerical performance on several test problems.

� TB02Room H005 - Tuesday 13:30–15:00

ClusterOptimization in Chemical EngineeringOrganizers: I. Grossmann, L.T. Biegler

Dynamic Optimization in Chem-ical Process SystemsInvited sessionChair: Lorenz T. Biegler

1. Optimizing an intensive energeti-cally integrated cryogenic process

Marıa Soledad Dıaz, PLAPIQUI, Universidad Na-

cional del Sur, Camino La Carrindanga Km 7, Bahıa

Blanca, Argentina, sdiaz@plapiqui.edu.ar / Co-authors:

Juan Ignacio Laiglecia, Mariela Rodriguez, Patricia Hoch

We perform dynamic optimization of an integratedturboexpansion natural gas processing plant. Cryo-genic countercurrent heat exchangers with partialcondensation have been modeled through dynamicmass, energy and momentum balances in bothphases, and thermodynamics with the SRK equationof state. The demethanizer model includes pathconstraints on CO2 solubility in the upper stages.Dynamic separation vessels and static turboexpander

models have been included. The DAE optimizationproblem has been transformed into a large NLPapplying orthogonal collocation over finite elementsin time. An IP method with rSQP techniques isused. Optimization variables are top pressure inthe demethanizer and a bypass fraction in heatexchangers. The objective is to maximize ethanerecovery, when changing to a different operatingmode or when step and ramp changes are introducedin feed flowrate. Numerical results provide optimaltemporal and spatial profiles and have been com-pared to plant data, with good agreement.

2. Control vector parameterizationand metaheuristics for solving dynamicoptimization problemsJose Egea, Universidad Politecnica de Cartagena,

Paseo Alfonso XIII, 52, 30203, Cartagena, Spain,

josea.egea@upct.es / Co-author: Jose Ricardo Perez-

Correa

Global deterministic methods have been applied tosolve dynamic optimization prob-lems, but they canhandle limited types of path constraints, requirefunctions differenti-ability and are computationallyintensive. Alternatively, a special class of stochasticglobal optimization methods, called metaheuristics,have been successfully applied to solve a widerange of dynamic optimization problems. In thiscontribution we present a metaheuristic based onscatter search for the global dynamic optimizationof chemical engineering processes using the controlvector parameterization (CVP) approach. It isdesigned to overcome typical difficulties of non-lineardynamic systems optimization such as noise, flatareas, non-smoothness and/or discontinuities. It bal-ances intensifica-tion and diversification by includinga local search procedure which can accelerate theconvergence to the optimal solutions in some cases.The method has been applied to a set of dynamicoptimization benchmarks from the bioprocess engi-neering area. Its results compared well with thoseobtained by other optimization methods.

3. A filter trust region method for op-timization with reduced order processmodelsLorenz T. Biegler, Carnegie Mellon University, Chemi-

cal Engineering Department, Carnegie Mellon University,

Pittsburgh, PA 15213, USA, lb01@andrew.cmu.edu /

Co-author: Anshul Agarwal

TECHNICAL SESSIONS — TUESDAY 33

Process models, especially with partial differentialequations, can be prohibitively expensive for opti-mization. Instead, reduced order models (ROMs)are frequently constructed and applied for an op-timization study. Nevertheless, such models maynot capture all of the features of the more detailedmodel and may not provide sufficient accuracy toguarantee convergence to an optimum. Over thepast two decades trust-region methods have beendeveloped that can provide an adaptive frameworkfor ROM-based optimization. They not only restrictthe step around the root-point, but also synchronizeROM updates with the information obtained overthe course of optimization, thus providing a robustand globally convergent framework. In this talk,we develop two variants of ROM-based trust regionstrategies for process optimization. First, a classicalexact penalty-based trust-region algorithm is devel-oped, along with correction schemes for the objectiveand the constraints to ensure global convergencewith ROM-based approximate models. Next, wedevelop a filter-based approach, where infeasibilitiesand objective function improvement are traded ina multicriterion strategy. Such an approach hasfavorable convergence properties and overcomes thesensitivity to penalty parameters. These approachesare applied to challenging applications for thecapture of CO2 via gas adsorption. Both algorithmsare demonstrated for a two-bed four-step PSA casestudy for post-combustion capture. Here the detailedmodel is based on an expensive solution of multiplePDEs, while the ROM-based NLP is constructedfrom Principal Orthogonal Decomposition (POD)and can be solved very efficiently. In both cases, weobserve that the ROM-based algorithms converge toa local optimum of the original optimization problemwithin significantly improved performance.

� TB03Room H006 - Tuesday 13:30–15:00

ClusterNatural ResourcesOrganizers: P. Gajardo, V. Albornoz

Optimization in harvesting prob-lemsInvited sessionChair: Pedro Gajardo

1. Production planning model forthe salmon fresh water stage underuncertainty

Fernanda Bravo, University of Chile, Republica 701,

of. 302, Santiago, Chile, ma.fernanda.bravo@gmail.com

/ Co-authors: Guillermo Duran, Andres Weintraub

We present a production planning in the salmonfarming at the fresh water stage. The aim of theplanning is to satisfy the sea water demand forfishes at minimum cost possible during the timehorizon, considering culture capacities, operationalrestrictions and fish strains to be cultured. Themodel is built based on linear programming, whichhas been structured as a multi commodity flowproblem with capacity and flow transformationsthat represents the growth and mortality of thefishes during the culture period. Then, a stochasticprogramming model based on scenario analysis isdeveloped to evaluate the impact of the randomnessin the survival rate in planning. The main resultssuggest that stochastic approach is always the bestglobal solution under uncertainty, since the solutionis feasible in each scenario by construction, and incases of high variance among sceneries it is up to15% superior to the deterministic solution.

2. On the Mitra-Wan forestry model:a unified analysis

Adriana Piazza, Universidad Federico Santa Marıa, Av.

Espana 1680, Valparaıso, Chile, adriana.piazza@usm.cl /

Co-author: M. Ali Khan

We present a substantive and far-reaching general-ization of the principal results in the economics offorestry, as formalized by Mitra-Wan (1986). Ratherthan a polarized dichotomy of linear and strictlyconcave, differentiable benefit (felicity) functions, wedevelop the theory in the context of functions thatare supported at the golden-rule consumption andnot necessarily concave. Through a non-interioritycondition on the zeroes of a resulting “discrepancyfunction”, we show the equivalence of finitelymaximal, maximal, minimal value-loss and optimalprograms, and thereby answer questions left open byBrock and Mitra. Our synthesizing criterion is newto the capital-theory literature, and in the concavesetting, proves to be necessary and sufficient for theasymptotic convergence of good programs.

34 TECHNICAL SESSIONS — TUESDAY

3. Bargaining with intertemporalmaximin payoffs: formal problem andgeneral solution under monotonicity

Pedro Gajardo, Universidad Federico Santa Marıa, Av.

Espana 1680, Valparaıso, Chile, pedro.gajardo@usm.cl /

Co-authors: V. Martinet, M. De Lara, H. Ramırez

In this talk we describe a new class of dynamicproblems which are called “bargaining problemswith intertemporal maximin payoffs”. Such problemsmay reflect sustainability issues. Each bargainer (orstake-holder) has a representative indicator, namelya function of the state and decisions, and aims atmaximizing its minimal value over time. Bargainingon sustainability issues consists in defining theset of stake-holder’s payoffs. We are interestedin defining the feasibility set of outcomes of suchproblems. This set is interpreted as a support fora social choice sustainability rule. We provide itscharacterization in a general framework under somemonotonicity properties of the dynamics, consistentwith many economic problems and, in particular,“environmental economic” sustainability issues.

� TB04Room H104 - Tuesday 13:30–15:00

ClusterMathematical EconomicsOrganizers: J.M. Bonnisseau, J. Rivera

Game TheoryContributed & Invited sessionChair: Paulo K. Monteiro

1. A folk theorem with Markovianprivate information

Juan Escobar, Universidad de Chile, Chile, jesco-

bar@dii.uchile.cl/ Co-author: Juuso Toikka

We consider repeated Bayesian two-player gamesin which the players’ types evolve according toan irreducible Markov chain, type transitions areindependent across players, and players have privatevalues. The main result shows that, with commu-nication, any Pareto efficient payoff vector abovea minmax value can be approximated arbitrarilyclosely in a perfect Bayesian equilibrium as thediscount factor goes to one. As an intermediatestep we construct a dynamic mechanism (withouttransfers) that is approximately efficient for patientplayers given sufficiently long time horizon.

2. On the superiority of voluntaryvoting: a clean-cut result

Matteo Triossi, Universidad de Chile, Republica 701,

Santiago, Chile, mtriossi@dii.uchile.cl

This paper presents a strategic model of commonvalue elections with endogenous information acquisi-tion. It compares voluntary and compulsory voting.The main result shows that voluntary voting issuperior to compulsory voting in term of informationaggregation. Differently than in previous work thedifference is finite.

3. Games with discontinuous payoffs:a strengthening of Reny’s existencetheorem

Paulo K. Monteiro, EPGE-FGV, Brazil,

paulo.klinger@fgv.br / Co-author: Andrew McLen-

nan, Rabee Tourky

We provide a pure Nash equilibrium existencetheorem for games with discontinuous payoffs whosehypotheses are in a number of ways weaker thanthose of the theorem of Reny (1999). Our resultsubsumes a prior existence result of Nishimura andFriedman (1981) that is not covered by his theorem.In comparison with Reny’s argument, our proof isbrief.

� TC01Room H004 - Tuesday 15:30–17:00

PDE Constrained OptimizationContributed sessionChair: Sergio Gonzalez

1. Adaptive shape optimization for theinstationary Navier-Stokes equations

Christian Brandenburg, TU Darmstadt, Do-

livostr. 15, Germany, brandenburg@mathematik.tu-

darmstadt.de / Co-author: Stefan Ulbrich

We consider shape optimization problems governedby the incompressible instationary Navier-Stokesequations. We use an approach based on transforma-tions of a reference domain which is very flexible andallows arbitrary types of parametrizations. We firstpresent the general function space setting in whichcontinuous adjoint computations are used to obtainexact discrete gradients. This approach is appliedto problems governed by the incompressible insta-

TECHNICAL SESSIONS — TUESDAY 35

tionary Navier-Stokes equations. The continuousoptimization problem is discretized with the cG1dG0finite element method. The focus of this talk will beon multilevel optimization where we use adaptivitybased on goal-oriented error estimators with thedrag objective functional as quantity of interest.This allows for the efficient numerical solution of theshape optimization problems by performing mostoptimization iterations on coarse grids. We presentnumerical examples where we apply the developedtechniques to instationary, time-periodic flows in 2Dand 3D.

2. An extremal eigenvalue problem fora two-phase conductor in a ballLeon Sanz, DIM-CMM, Univ. de Chile, Av. Blanco

Encalada 2120, Santiago, Chile, lsanz@dim.uchile.cl /

Co-authors: Carlos Conca, Rajesh Mahadevan

We deal with the problem of distributing twoconducting materials in a given domain, with theirproportions being fixed, so as to minimize the firsteigenvalue of a Dirichlet operator. When the designregion is a ball, it is known that there is an optimaldistribution of materials which does not involvethe mixing of the materials. However, the optimalconfiguration even in this simple case is not known.As a step in the resolution of this problem, in thispaper, we develop the shape derivative analysisfor this two-phase eigenvalue problem in a generaldomain.

3. Multigrid second-order accurate so-lution of parabolic control-constrainedproblems

Sergio Gonzalez Andrade, Escuela Politecnica

Nacional, Lugo N24-407 y Coruna, Ecuador, sgonza-

lezandrade@gmail.com / Co-author: Alfio Borzi

A mesh-independent and second-order accuratemultigrid framework to solve parabolic optimal con-trol problems is presented. The resulting algorithmsappear to be robust with respect to change of valuesof the control parameters and have the ability toaccommodate constraints on the control also in thelimit case of bang-bang control. Central to thedevelopment of these multigrid schemes is the designof iterative smoothers which can be formulated aslocal or block semismooth Newton methods. Thedesign of distributed controls is considered to drivenonlinear parabolic models to follow optimally a

given trajectory or attain a final configuration. Inboth cases, results of numerical experiments andtheoretical twogrid local Fourier analysis estimatesdemonstrate that the proposed schemes are able tosolve parabolic optimality systems with textbookmultigrid efficiency. Further results are presented tovalidate second-order accuracy and the possibility totrack a trajectory over long time intervals by meansof a receding-horizon approach.

� TC02Room H005 - Tuesday 15:30–17:00

Nonlinear Programming Algo-rithms IContributed sessionChair: Frank E. Curtis

1. A unified local convergence analysisof inexact constrained Levenberg-Marquardt methodsRoger Behling, IMPA, Avenida Atlantica 2806, Ap.

1104, 22070-000, Copacabana, Rio de Janeiro, Brazil,

rogerb@impa.br / Co-author: Andreas Fischer

The Levenberg-Marquardt method is a regularizedGauss-Newton method for solving systems of non-linear equations. If an error bound condition holdsit is known that local quadratic convergence to anon-isolated solution can be achieved. This resultwas extended to constrained Levenberg-Marquardtmethods for solving systems of equations subject toconvex constraints. In this talk we present a localconvergence analysis for an inexact version of a con-strained Levenberg- Marquardt method. We showthat the best results known for the unconstrainedcase also hold for the constrained Levenberg-Marquardt method. Moreover, the influence of theregularization parameter on the level of inexactnessand the convergence rate is described. This workimproves and unifies several existing results on thelocal convergence of Levenberg-Marquardt methods.

2. A new trust-region Gauss-Newtonmethod for nonlinear feasibility prob-lems and bound-constrained nonlinearleast-squaresMargherita Porcelli, FUNDP-University of Namur,

Dept of Math., rue de Bruxelles, 61 - 5000 NAMUR,

Belgium, margherita.porcelli@fundp.ac.be / Co-authors:

Maria Macconi, Benedetta Morini

We address the solution of nonlinear feasibility

36 TECHNICAL SESSIONS — TUESDAY

problems stated as systems of nonlinear equalitiesand inequalities. Such systems arise in a widevariety of problems such as model formulationdesign, parameter identification problems, detectionof feasible points in nonlinear programming. Wepresent a new approach that consists in transform-ing the system into a suitable bound-constrainednonlinear least-squares problem and solving itby a trust-region Gauss-Newton method. Thenew method offers global convergence propertiescombined with potentially fast local convergence.The implementations of the trust-region strategyinvolve a linear algebra phase; we discuss the use ofmatrix factorizations and CG-like methods for suchphase. A new Matlab solver, TRESNEI, that relieson matrix factorizations is provided together withthe numerical comparison with functions from theMatlab Optimization Toolbox. Finally, we presentpreliminary numerical experiments on large-scaleproblems, carried out with a Fortran 95 implemen-tation of the new method.

3. A penalty-interior-point algorithmfor nonlinear optimization

Frank E. Curtis, Lehigh University, 200

W. Packer Ave., Bethlehem, PA 18015, USA,

frank.e.curtis@gmail.com

An algorithm for nonlinear optimization thatcombines penalty and interior-point techniques ispresented. The novelty of the method, in contrastto many previously proposed penalty-interior-pointalgorithms, is that the main focus of the approachis the updating scheme for the penalty and interior-point parameters. We motivate our method, discussits convergence properties, and illustrate its robustand efficient practical behavior, especially on ill-conditioned and infeasible problem instances.

� TC03Room H006 - Tuesday 15:30–17:00

ClusterNatural ResourcesOrganizers: P. Gajardo, V. Albornoz

Optimization of wastes manage-ment and bioprocesses

Contributed sessionChair: Raul Conejeros

1. Optimal solid waste management inurban areas

Nekram Rawal, Motilal Nehru National Institute of

Technology, Alllahabad, C-62, staff Colony, MNNIT,

India, nrrawal@mnnit.ac.in / Co-authors: Raj Mohan

Singh, R.C. Vaishya

Solid wastes are major consequence of urbanizationand development, and have emerged a serious threatto environment. Safe and effective management ofsolid waste generated by community and govern-mental as well as commercial institutions is the needof the hour. Improper disposal of solid wastes mayadversely affect environment and human health.Solid waste management (SWM) is needed for thesolution of the problem of solid waste concerningprotection of the environment and conservationof natural resources. The selection of a suitableSWM mainly involves the collection of waste fromits sources and the transportation of waste toprocessing plants where it can either be convertedinto refuse derived fuel (RDF), electrical energy,compost (stabilised organic material) or recycledfor reuse. The unrecoverable waste can either betransported directly from the waste sources tolandfills or from treatment plants to landfills. Acareful planning is required in order to execute theseactivities in an optimal way. Data from an Indianurban city, Allahabad city, is utilized to demonstratethe application of the proposed methods. Themathematical formulation of the optimization modelwas solved using commercially available optimizationsoftware Lingo 10.0. Performance evaluation resultsof optimization models for the MSW establishedpotential application of the methodology for solidwaste management in urban areas.

2. A conceptual model for optimalexploration of scenarios for managingwater in the Mojana Colombia

Eddy Herrera, Pontificia Universidad Javeri-

ana, Cr7 No 42-62 Edi 52 ofc 604, Colombia,

eherrera@javeriana.edu.co / Co-authors: Alejandro

Franco, Nelson Obregon

The problem of seasonal flooding in the area of theMojana Colombia, is very complex and dependent onenvironmental and social geomorphological factorsthat are interrelated. This leads to the formulationof a multicriteria optimal model that from segmentdata to simulate the system’s response to a recon-

TECHNICAL SESSIONS — TUESDAY 37

figuration of the drainage network, and additionalvalues its impact on population, environment andland use. Consequently, this paper develops a con-ceptual model of optimal multi-criteria explorationof scenarios for optimal management of water inMojana Colombia, and also implement sustainabilityindicators to assess system response to changes inthe drainage system and assess its impact on thepopulation environmental and land use.

3. Trajectory validation of ordinarydifferential equations

Raul Conejeros, Pontificia Universidad Catolica de

Valparaıso, Av. Brasil 2950, Valparaıso, Chile, rcone-

jer@ucv.cl / Co-author: Felipe Scott

This work proposes a methodology based on optimalcontrol for the trajectory validation of ordinarydifferential equations, under parametric uncertainty.Thus, simulation results under uncertainty may yieldsuperior and inferior trajectories, not determinedby extreme interval values of the parameters. Itis proposed that considering an optimal controlproblem, where the uncertain parameters are takenas controls, for a number of intervals, the value of thecontrols can be determined, so that the trajectoriesare maximized or minimized to find the superior andthe inferior ones, respectively. Although a determin-istic solution to this problem is presented, a globallyvalid one cannot be found in this way. A heuristic isproposed as well, by further refinement by doublingthe number of the intervals until changes in superiorand inferior trajectory defining parameter values arenot detected. This work has been funded by theresearch grant FONDECYT 1080118.

� TC04Room H104 - Tuesday 15:30–17:00

ClusterMathematical EconomicsOrganizers: J.M. Bonnisseau, J. Rivera

Contract TheoryContributed & Invited sessionChair: Andres Carvajal

1. Energy contracts managements, op-timal decision and sensibility analysis

Zhihao Cen, CMAP, Ecole Polytechnique, France,

zhihao.cen@polytechnique.edu / Co-authors: Joseph

Frederic Bonnans, Thibault Christel

We consider the problem of optimal management ofenergy contacts, with bounds on the local (time step)amounts and global (whole period) amounts to betraded, and uncertainty on prices only. After build-ing a finite state Markov chain by using vectorialquantization tree method, we rely on the stochasticdual dynamic programming method to slove thisstochastic optimization problem. Combining theprevious techniques, we are able to deal with highdimension state variable problems. Numerical testsare applied to realistic energy markets problems havebeen performed. Finally, some sensibility analysis,used in searching corresponding hedging strategies,are also discussed.

2. Dynamic contracts under loss aver-sion

Andrea Repetto, Universidad Adolfo Ibanez, Diagonal

Las Torres 2640, Santiago, Chile, andrea.repetto@uai.cl

/ Co-authors: Alejandro Jofre, Sofıa Moroni

We extend the dynamic moral hazard principal-agentmodel to allow for an agent who is loss averse andwhose reference updates according to previous con-sumption. When the agent has no access to creditmarkets, the optimal payment scheme can have flatsegments at the reference level. This property im-plies that there is a positive probability of observingconstant wages over time, even though the schemehas memory. Moreover, the model predicts a statusquo bias whenever the agent is allowed to borrow orsave after the outcome is realized -a gap between theinterest rates at which the agent is willing to lendand borrow. We also show that although the optimalcontract scheme is renegotiation-proof, it cannotbe implemented by a sequence of spot contracts.However, when the agent has access to the creditmarket and the principal can monitor savings, thelong-term optimal contract is spot contractible.

3. Bundling without price discrimina-tion

Andres Carvajal, University of Warwick, U.K,

A.M.Carvajal@Warwick.ac.uk. / Co-author: Marzena

Rostek and Marek Weretka

This paper examines the optimal bundling strategiesof a multiproduct monopoly in markets where a sellercannot monitor and, hence, restrict the purchasesof buyers to a single bundle while buyers have

38 TECHNICAL SESSIONS — WEDNESDAY

resale opportunities. In such markets, the standardmechanism through which bundling increases sellerprots, based on price discrimina- tion, is not feasible.The prot-maximizing bundling strategy is character-ized, given the restrictions on pricing policies thatresult from resale and a lack of monitoring. Welfareimplications of optimal bundling are analyzed.

WEDNESDAY

� WA01Room H004 - Wednesday 10:30–12:00

Mathematical Models for DataMining and Game TheoryInvited sessionOrganizer/Chair: Richard Weber

1. Adversarial classification with dy-namic games of incomplete information

Gaston L’Huillier, Universidad de Chile, Republica

701, Santiago, Chile, glhuilli@dcc.uchile.cl / Co-authors:

Nicolas Figueroa, Richard Weber

In adversarial learning environments, the interactionbetween a classifier and adversaries can be modeledas a game between two players. This approach hasbeen previously proposed as a static game withcomplete information. It seems to be more realistic,however, to model the incremental interactions as adynamic game of incomplete information, for whichits equilibrium strategies can be approximated, andconsidered as input for the classification task. Inthis paper, we show how to model such interactionsbetween players, as well as directions on how toapproximate their mixed strategies, and considerthe minimization of the classification function’sempirical risk. Results, showed competitive resultsagainst benchmark online learning algorithms.

2. Fast and correct: classification withadvanced support vector machines

Richard Weber, DII, Universidad de Chile, Republica

701, Santiago, Chile, rweber@dii.uchile.cl / Co-authors:

Jaime Miranda, Daniel Espinoza

Many applications require the analysis and classifi-cation of large data sets. Several methods exist forthis task being Support Vector Machines (SVM) ofparticular interest from an optimization point-of-

view. We present an heuristic approach that usescolumn generation for linear SVM with an updatingscheme for the objective function which reducesconsiderably computational time and at the sametime allows lower classification errors.

3. Strategic costs in a specific locationmechanism to NIMBY

Fernando Crespo, Universidad de Valparaıso,

Brigadier de La Cruz 1050, San Miguel, Santiago, Chile,

fernando.crespo@uv.cl

NIMBY (Not In My Back Yack) are facilities nec-essary to society, but rejected by communities thathost them. We developed a specific mechanism forNIMBY location using auctions over costs declaredby the respective communities. The mechanismis efficient, budget-balanced, maintains the ratio-nality conditions, is not incentive compatible, butit maintains the ranking of true costs. For thismechanism, we calculate the strategic declaredcosts for communities using specific probabilitydistributions. We compare our approach with otherclassical results of strategic declarations in auctionmechanisms. This step is necessary to simulate casesin real applications of NIMBY location.

� WA02Room H005 - Wednesday 10:30–12:00

Derivative Free Optimization:AlgorithmsContributed sessionChair: Anke Troeltzsch

1. Derivative free inexact-restorationalgorithm for constrained optimization

Marıa Belen Arouxet, Universidad Nacional de La

Plata- CONICET, Argentina, belenarouxet@gmail.com

/ Co-authors: Nelida Echebest, Elvio Pilotta

Derivative free optimization methods are designedfor solving nonlinear programming problems wherethe derivatives of the objective function and theconstraints are not available because they comefrom industrial measure or are the results of largecomputer simulation. We propose a new algorithmfor nonlinear programming problems without deriva-tives based on the Inexact Restoration methods,which was introduced by Martınez and Pilotta(2000). These methods proceed in two phases and

TECHNICAL SESSIONS — WEDNESDAY 39

generate a sequence of generally infeasible iterateswith intermediate iterations that consist of inexactlyrestored points. In our approach, all the derivativescalculations are performed by suitable modifications.We also present numerical experiments.

2. Admissible design of computerexperiments for constrained DFO

Frederic Delbos, IFP, 1&4 Avenue de Bois-Preau,

92500 Rueil-Malmaison, France, frederic.delbos@ifp.fr

In optimization problems for geosciences appli-cations, simulators are often computational timeexpensive black-boxes that do not provide anyderivatives. These optimization problems are sub-mitted to inequality constraints, among which someof linear constraints, namely the “hard” constraints,have to be strictly respected to avoid unrealisticvalues or even a crash of the simulator. In thiscontext, we have adapted a standard SQP algorithmwith approximated derivatives by linear interpo-lation models of objective function and nonlinearconstraints. We present an algorithm for the choiceof interpolation points in the vicinity of the currentSQP iterate. This algorithm tries to conciliate threeobjectives: ensure well posedness for linear interpo-lation problems, minimize the number of additionalpoints to be simulated (using as many previoussimulated points as possible), and choose them tobe strictly admissible for “hard” constraints. Thisalgorithm is applied to a parameter identificationproblem in reservoir engineering field.

3. A subspace trust-region methodfor bound-constrained derivative-freeoptimization

Anke Troeltzsch, CERFACS, 42 avenue G. Coriolis,

France, anke.troeltzsch@cerfacs.fr / Co-authors: Serge

Gratton, Philippe L. Toint

Several trust-region based algorithms have been pro-posed to minimize a function, in the case where itsderivatives are not available or are computationallyprohibitive. The algorithms we are interested in,typically minimize a polynomial interpolation modelinside a trust region. The geometry of the set ofinterpolation points, as measured by the poisednessof the set, must be satisfactory. A new variantof derivative-free algorithm has been proposed inScheinberg and Toint (2009) as an attempt toreduce as much as possible the recourse to geometry

improving steps, while maintaining a mechanismto take geometry into account. We extended thealgorithm to handle bounds and propose applyingan active-set method where the step is limited tothe current set of active variables. We show how toalgorithmically apply this technique to maintain agood convergence behaviour and demonstrate theefficiency of our approach on problems from theCUTEr library.

� WA03Room H006 - Wednesday 10:30–12:00

Electricity Portfolio Manage-mentInvited sessionOrganizer/Chair: Laetitia Andrieu

1. Continuous formulation of a electricpower management problem

Kengy Barty, EDF R&D, OSIRIS R36, 1 avenue

du General de Gaulle 92141 Clamart cedex, France,

kengy.barty@edf.fr

The electric power management problem raises manydifficulties. Indeed this problem aims to planifyelectrical production minimizing the productioncost. This problem is too large to be tackled withits entire complexity, so we will concentrate on thefollowing question, which is the optimal date to stopthe engine for refuelling. This economical problemis really important so far, because the decision tochange the date of begining of a stop may inducevery importants cash-flow. That’s why it is reallyimportant to integrate this economical parameterfor calculating optimal decisions. Unfortunately theintrisic nature of this problem prevents us to derivesensitivity of optimal cost according of the date ofstop which is an integer variable. We propose areformulation of this problem and we show how thisnew formulation can help us to bypass the difficultywe have mentioned.

2. Dual approximate dynamic pro-gramming for stochastic optimal con-trol problems

Pierre Girardeau, CERMICS, Universite Paris-Est,

6-8 avenue Blaise Pascal, 77455 Marne la Vallee Cedex

2, France, pierre.girardeau@cermics.enpc.fr / Co-author:

Kengy Barty

We consider a dynamical system driven by exogenous

40 TECHNICAL SESSIONS — WEDNESDAY

noises and decisions at each time step, based on theobservation of the history of the system up to thecurrent time step. In the Dynamic Programmingframework, the main challenge of the problems weconsider is to bypass the curse of dimensionality. Toovercome this difficulty, we propose a decompositionmethodology using Lagrangian relaxation. Evenwhen the problem satisfies the classical assumptionsrequired for the convergence of the decompositionscheme, an extra difficulty arises in the contextof stochastic optimal control: the dual variable isa general stochastic process and hence the reso-lution of subproblems by Dynamic Programmingis intractable in general. We propose to solvesubproblems by restraining the memory (or theinformation) on the dual process. We establish a linkbetween these approximations and how the couplingconstraint may be satisfied in the original problem.

3. Continuous optimization in theenergy industry

Laetitia Andrieu, EDF, 1 avenue du General de

Gaulle, 92141 Clamart, France, laetitia.andrieu@edf.fr

Liberalization of energy markets displays new issuesfor electrical companies which now have to masterboth traditional problems (such as optimization ofelectrical generation) and emerging problems (suchas integration of financial markets). Several of theseproblems often require continuous optimizationtechniques. In this talk, we present some of theseproblems for which we give a brief descriptionof the modeling and the optimization techniquesthat are applied to them: scenario decomposition(by progressive hedging or Lagrangian relaxation),price decomposition, dual methods for multistagestochastic programming,...

� WA04Room H104 - Wednesday 10:30–12:00

Multiobjective optimizationContributed sessionChair: Douglas Vieira

1. Direct-multisearch (DMS) for mul-tiobjective optimization

Ana Luisa Custodio, New University of Lisbon,

Dept. Mathematics FCT-UNL Quinta da Torre 2829-516

Caparica, Portugal, alcustodio@fct.unl.pt / Co-authors:

Jose Aguilar Madeira, Ismael Vaz, Luis N. Vicente

DMS is a novel derivative-free algorithm for mul-tiobjective optimization, which does not aggregateany of the objective functions. Inspired by thesearch/poll paradigm of direct-search, DMS uses theconcept of Pareto dominance to maintain a list ofnondominated points, from which the new iteratesor poll centers are chosen. The aim is to generateas many points in the Pareto frontier as possiblefrom the polling procedure itself, while keeping thewhole framework general to accommodate otherdisseminating strategies, in particular when usingthe (here also) optional search step. We prove underthe common assumptions used in direct search forsingle optimization that at least one limit point ofthe sequence of iterates lies in the Pareto frontier.Computational results are reported on a test set ofmultiobjective problems, showing that our method-ology has an impressive capability of generating thewhole Pareto frontier even without using a searchstep.

2. An ellipsoid based method for mul-tiobjective optimization problems

Douglas Vieira, ENACOM - Handcrafted Tech-

nologies, R. Rita Nunes Leite, 135, Brazil, dou-

glas.vieira@enacom.com.br / Co-authors: Adriano

Lisboa, Rodney Saldanha

This work introduces some modifications requiredto the classical Shor’s ellipsoid method to dealwith multiobjective optimization problems. If allobjectives are used to generate cutting-planes, somecan generate invalid cuts that exclude the wholePareto optimal set from the localizing set, even ifstrict convexity is considered. The ellipsoid methodis modified in order to handle simultaneous cuts andto filter the invalid cuts. The novel formulation in-creases the algorithm convergence while maintainingthe guarantees of convergence under the assumptionof pseudo-differentiability of the objectives andconstraints. An application to antenna design ispresented.

3. On line search methods for multiob-jective optimization

Douglas Vieira, ENACOM - Handcrafted Tech-

nologies, R. Rita Nunes Leite, 135, Brazil, dou-

glas.vieira@enacom.com.br / Co-authors: Adriano

Lisboa, Rodney Saldanha

TECHNICAL SESSIONS — WEDNESDAY 41

This paper discusses achievable and desired prop-erties for line searching in multiobjective problems.The main difference between the single and multi-objective cases lies in the fact that a point in a set,instead of a single point (e.g. considering strictlyeconvexity), is the algorithm output. This feature isused to build a golden section like method whichhas a faster convergence rate when compared to thetraditional single objective one. Furthermore, themultiobjective golden section is compared with amultiobjective version of the Armijo s rule for someanalytical problems.

� WB01Room H004 - Wednesday 13:30–15:00

Linear, Semidefinite and ConeOptimizationInvited sessionOrganizers: Florian Jarre, Hector RamırezChair: Florian Jarre

1. Accelerated projection methods forsemidefinite programs

Florian Jarre, Universitat Dusseldorf, Universitatsstr.1,

40225 Dusseldorf, Germany, jarre@opt.uni-duesseldorf.de

In an earlier joint work with Franz Rendl, a firstorder method for solving semidefinite programsbased on an augmented primal dual function hasbeen analyzed. A drawback of this approach wasa rather slow convergence behavior close to theoptimal solution. In this talk, both, theoretical andnumerical results of this approach are improved.The implementation uses the augmented primaldual function to generate an approximate optimalsolution and then applies a preconditioned QMRiteration to improve this approximation.

2. On stability of perturbed second-order cone programs

Hector Ramırez, Universidad de Chile, Av. Blanco

Encalada 2120, Santiago, Chile, hramirez@dim.uchile.cl

/ Co-authors: Jiri Outrata

We characterize the Aubin property of the criticalsolution set of a canonically perturbed second-ordercone programming problem (SOCP) in terms ofa strong second-order optimality condition. Thiscondition requires the positive definiteness of aquadratic form, involving the Hessian of the La-grangian and an extra term associated with the

curvature of the constraint set, over the linear spacegenerated by the cone of critical directions. Sincethis condition is equivalent to the strong regularity,the critical solution set in (SOCP) behaves similarlyas in nonlinear programming.

3. Existence and stability results forthe semidefinite linear complementar-ity problem

Ruben Lopez, Universidad Catolica de la Santısima

Concepcion, Facultad de Ingenierıa, Campus San Andres,

Alonso Ribera 2850, Concepcion, Chile, rlopez@ucsc.cl /

Co-authors: Hector Ramırez, Julio Lopez

In this work we study the semidefinite linear com-plementarity problem SDLCP by describing theasymptotic behavior of the approximate solutionsto its equivalent variational inequality formulation.Thus, we establish some properties satisfied bythe directions which are limits of the normalizedunbounded approximate solutions. Based on thisproperties, coercive/noncoercive existence conditionsand stability results for SDLCP’s are given. Weintroduce the class of Garcıa linear transformationsthat generalize that from the linear complementarityproblem. Our approach allows us to deal withvarious linear transformations from the literature ina unified framework. In addition, some estimates forthe asymptotic cone of the solution set, for differentclasses of linear transformations, are given as well.Hence, the present approach sheds new light andoffers an alternative way to view some known results.

� WB02Room H005 - Wednesday 13:30–15:00

Derivative Free Optimization:ApplicationsContributed sessionChair: Patrick Laloyaux

1. Handling constraints for derivativefree optimization problems

Hoel Langouet, IFP, 1-4 avenue de Bois-Preau,

92852 Rueil-Malmaison, France, hoel.langouet@ifp.fr

Co-authors: Delphine Sinoquet, Sebastien Da Veiga

Optimization techniques for optimization underconstraints takes place in various application fields:inverse problems in geosciences, engine calibration,...The underlying optimization problems require ded-

42 TECHNICAL SESSIONS — WEDNESDAY

icated techniques for derivative free optimizationunder derivative free constraints in order to limit thenumber of evaluations of the usually time consumingsimulator. We propose the Sequential QuadraticApproximation method (SQA) based on successiveminimizations in a trust region of a quadraticinterpolating model of the objective function underquadratic interpolating models of the inequalityconstraints. The efficiency of this approach isdemonstrated on the benchmark MOPTA08 (Jones,2008). SQA method is applied on an industrialapplication: the reservoir characterization inverseproblem for forecasting the oil production of afield from available data. These data (pressure,oil/water/gas rates at wells and 4D seismic data) arecompared to simulated data (fluid flow simulationsand petrophysical models) to determine petrophysi-cal properties of the reservoir.

2. Engine calibration: a constrainedderivative free optimization problem

Delphine Sinoquet, IFP, 1&4 avenue Bois-Preau

92852 Rueil-Malmaison, France, delphine.sinoquet@ifp.fr

/ Co-authors: Hoel Langouet, Gregory Font, Sebastien

Magand, Fabien Chaudoye, Michel Castagne

Nowadays, automotive manufacturers are submittedto strong constraints in engine calibration: lowestfuel consumption, emission-control legislation anddriver requests for driving comfort and performances.These constraints lead to an increasingly complexityof the underlying optimization problem. A classicalmethod is based on response surface methodology forexperiments at test bench in stabilized conditions.In this approach, the transient effects during thecycle are not taken into account. A promising ideais to use physical modelling of the engine (to getthe conditions in the combustion chamber beforecombustion: gas composition, injection behaviour,...)coupled with statistical models to obtain engine-outemissions. A dedicated parameterization of theengine maps and a Derivative Free Optimizationmethod is then used to minimize the cumulatedfuel consumption and pollutant emissions, undercombustion noise constraints, on a driving cycle. Anapplication on a real dataset obtained at automatedtest-bench for a diesel engine are presented.

3. Derivative-free methods for largenonlinear data assimilation problems

Patrick Laloyaux, University of Namur, 8,

Rempart de la Vierge, 5000 Namur, Belgium,

patrick.laloyaux@fundp.ac.be / Co-authors: Serge

Gratton, Annick Sartenaer, Jean Tshimanga

Data assimilation is a concept involving any methodwhich estimates the initial state of a dynamicalsystem by combining both the information fromobservations and from a model operator whichintegrates a set of partial differential equationsthat describes the evolution of the system. Eval-uating derivatives in these problems is challengingas one needs to compute the Jacobian of themodel operator and its transpose which implies thederivation of a tangent linear and adjoint code.The Ensemble Kalman Filter (EnKF) providesa suitable derivative-free alternative by using aMonte-Carlo implementation on the Kalman filterequations. In this talk, we compare this alternativewith derivative-free optimization software wherethe number of variables has been reduced sincethe optimization is applied on a reduced subspacebased on the information contained in well-chosenempirical orthogonal functions of the system.

� WB03Room H006 - Wednesday 13:30–15:00

Engineering Optimization IContributed sessionChair: Esteve Codina

1. Classification of satellite imagesusing genetic algorithms

Eddy Herrera, Pontificia Universidad Javeri-

ana, Cr7 No 42-62 Edi 52 ofc 604, Colombia,

eherrera@javeriana.edu.co / Co-author: Julio Garcıa

Traditionally, the unsupervised classification ofimages divides the pixels of an image pixel by pixelto assign the corresponding class. The number ofclasses usually has to be fixed a priori, based on thespectral properties of images and expert knowledge.This paper presents an alternative option based ongenetic algorithms (GA) to determine the optimalnumber of clusters through the generation of DaviesBouldin’s index applied to satellite imagery obtainedfrom space mission GEOS, which correspond tothree types: visible, infrared and water vapor.

TECHNICAL SESSIONS — WEDNESDAY 43

2. A maximin problem on a polyhedralset of connected variables

Alexander Belenky, Department of Mathematics

for Economics, National Research University-Higher

School of Economics, Moscow, Russia, and Center

for Engineering Systems Fundamentals, Massachusetts

Institute of Technology, Cambridge, Massachusetts,

USA, abelenky@mit.edu

The problem of finding a maximin of a minimumfunction of three vector variables is considered. Onevariable belongs to a polyhedron, whereas the othertwo belong to another polyhedron, and the functionis bilinear with respect to the first variable and toa pair of the other two variables. Under certainconditions imposed on both polyhedra, an auxiliaryminimum function becomes continuous on a polyhe-dral subset of the second polyhedron, which reducesthe initial problem to finding a minimum of themaximin of the bilinear function on the first polyhe-dron. Examples demonstrating the substantiality ofthe conditions for the equivalency of the two prob-lems and methods for finding the minimaximin onpolyhedra satisfying these conditions are discussed.The problem under consideration is a mathematicalmodel for a set of problems of estimating parametersin various systems. Examples of such problemsappearing in elections, transportation, and publicprocurement are presented.

3. A class of fixed point problems andits connection with the strategy basedcongested transit assignment model

Esteve Codina, Universitat Politecnica de Catalunya,

C/Jordi Girona 1-3 C5216, 08034 Barcelona, Spain,

esteve.codina@upc..edu

A class of fixed point problems for set valued func-tionals defined by optimization problems with rathergeneral structure are analyzed and reformulatedas variational inequality problems. A relevant andparticular instance of these problems is the congestedpassenger transit assignment model due to Cepeda,Cominetti and Florian. During the presentation,a reformulation of this transit assignment modelis done showing that it can be expressed as avariational inequality problem. The potentials ofthis formulation using variational inequalities areexplored, specially in the context of algorithmicmethods already existent for variational inequalities.Also an approximated model is formulated also in

V.I. using smoothing functions. The application ofmethods of averaging is shown for the case of strictcapacitated problems

[1] M. Cepeda, R. Cominetti and M. Florian, “A

frequency-based assignment model for congested transit

networks with strict capacity constraints: characteri-

zation and computation of equilibria”, Transportation

Research B 40 437-459 (2006).

� WB04Room H104 - Wednesday 13:30–15:00

Global OptimizationContributed sessionChair: Daniel Scholz

1. Direct search for linearly con-strained global optimization usingdifferent search steps

Ismael Vaz, University of Minho, Campus de Gualtar,

Portugal, aivaz@dps.uminho.pt / Co-authors: Luis N.

Vicente, Hoai An Le Thi

In this talk we address the derivative-free globaloptimization of functions subject to bound and linearconstraints, using different techniques in the searchstep of direct-search methods. A first approach isthe use of particle swarm for dissemination of pointsin the feasible region. A second technique consistsof using models based on radial basis functions(RBFs). Here, we also study the application ofalgorithms based on dc programming (difference ofconvex functions) for the minimization of the RBFmodels subject to simple bounds on the variables.Extensive numerical results are reported with a testset of bound and linearly constrained problems.

2. On a cutting plane concave min-imization algorithm for computingrobust regression estimators

Salvador Flores, Institut de Mathematiques de

Toulouse, Universite Paul Sabatier,118 route de

Narbonne, F-31062 Toulouse Cedex 9, France,

salvador.flores@math.univ-toulouse.fr

Robust statistics is a branch of statistics dealingwith the analysis of data containing large portionsof contaminated observations. The origin of suchcontamination can be very diverse; examples areerror measurements, anomalous individuals or unex-pected subpopulations not considered by the model.

44 TECHNICAL SESSIONS — WEDNESDAY

Therefore, it is impossible to make assumptions onthe magnitude nor on the structure of the contami-nation. The robustness of an estimator is measuredby means of the breakdown point, which is definedas the minimum fraction of observations that, ifreplaced by arbitrary data, can take the estimatorout of any bound. In this talk we will focus on theLeast Trimmed Squares (LTS) estimator, which isdefined as the best least squares fit to a half of theobservations. The computation of the LTS involves aconcave minimization problem, for which we proposea cutting plane algorithm.

3. The rate of convergence in geometricbranch-and-bound solution methods

Daniel Scholz, Georg-August-University Gottingen,

Lotzestr. 16-18, Germany, dscholz@math.uni-

goettingen.de / Co-author: Anita Schobel

Geometric branch-and-bound methods are popularsolution algorithms for non-convex global optimiza-tion problems with a small number of variables whichis given for instance in facility location problems.The main task throughout these branch-and-boundalgorithms is the calculation of some required lowerbounds. Several quite different techniques to do socan be found in the literature, among them methodsfrom interval analysis, d.c. programming, or somemore general frameworks. The aim of this talk isto analyze the quality of these bounds from thetheoretical point of view. To this end, we introducea definition for the rate of convergence in geometricbranch-and-bound methods and we calculate theserates for several bounding operations. Furthermore,our theoretical findings are justified by some numer-ical studies using facility location problems.

� WC01Room H004 - Wednesday 15:30–17:00

Geometry and Optimization IIInvited sessionOrganizer/Chair: Jorge Vera

1. Multiple bandgaps optimization oftwo-dimensional photonic crystals viasemidefinite programming and sub-space methods

Robert Freund, MIT, 50 Memorial Drive, Cambridge,

MA 02142, USA, rfreund@mit.edu / Co-authors: H.

Abby Men, N.C. Nguyen, Pablo Parrilo, Jaime Peraire

The mathematical formulation of the multi-ple bandgaps optimization problem leads to aninfinite-dimension Hermitian eigenvalue optimiza-tion problem parameterized by dielectric materialand the wave vector. To make it tractable, theproblem is discretized using the finite elementmethod into a series of finite-dimensional eigenvalueproblems. The resulting optimization problem islarge-scale and non-convex, with low regularity andnon-differentiable objective. By restricting to ap-propriate eigen-subspaces, we reduce the large-scalenon-convex optimization problem via reparametriza-tion to a sequence of small-scale convex semidefiniteprograms (SDPs) for which modern SDP solvers canbe efficiently applied. Among several illustrationswe show that it is possible to achieve optimizedphotonic crystals which exhibit multiple absolutebandgaps for the combined transverse electric andmagnetic modes. The optimized crystals showcomplicated patterns which are far different fromexisting photonic crystals. The Pareto frontier iscalculated to demonstrate the trade-off between twodifferent absolute bandgaps.

2. Randomized interior point methodsfor sampling and optimization

Hariharan Narayanan, MIT, 32D-566, 77 Mas-

sachusetts Avenue, Cambridge MA 02139, USA,

har@mit.edu

We present a Markov chain (Dikin walk) for samplingfrom a convex body equipped with a self-concordantbarrier, whose mixing time from a “central point” isstrongly polynomial in the description of the convexset. The mixing time of this chain is invariantunder affine transformations of the convex set, thuseliminating the need for first placing the body in anisotropic position. On every convex set of dimensionn, there exists a self-concordant barrier whose “com-plexity” is polynomially bounded. Consequently, arapidly mixing Markov chain of the kind we describecan be defined on any convex set. We use theseresults to design an algorithm consisting of a singlerandom walk for optimizing a linear function on aconvex set. We show that this random walk reachesan approximately optimal point in polynomial timewith high probability and that the correspondingobjective values converge with probability 1 to theoptimal objective value as the number of steps tendsto infinity.

TECHNICAL SESSIONS — WEDNESDAY 45

3. Problem geometry and problemrobustness in convex optimization

Jorge Vera, Universidad Catolica de Chile, Dept. In-

genierıa Industrial y de Sistemas, Escuela de Ingenierıa,

Santiago Chile, jvera@ing.puc.cl

The geometry of a set has been shown to explaincomplexity properties of some convex optimizationalgorithms and other measures like condition num-bers have similar properties. But condition numbersfor optimization also affect sensitivity of optimalsolutions with respect to changes in the data, soit is a relevant question whether the geometry ofthe feasible set also affects sensitivity of solutions.In this work we study some of those connectionsand address its potential implications for the com-putation of robust solutions. Robust solutions areprotected from data variation, but the change in therobust solution with respect to nominal solutionsis related to the robustness and well posedness ofthe problem itself. We show how some geometricmeasures of the feasible set could be used as a way ofassessing this robustness and how to estimate them.

� WC02Room H005 - Wednesday 15:30–17:00

Nonlinear Programming Algo-rithms IIContributed sessionChair: Joshua Griffin

1. A sufficiently exact inexact Newtonstep based on reusing matrix informa-tion

Anders Forsgren, Royal Institute of Technology

(KTH), Department of Mathematics, KTH, SE-100 44

Stockholm, Sweden, andersf@kth.se

Solving a nonlinear equation by Newton steps is aclassical method. We derive inexact Newton stepsthat lead to an inexact Newton method in which theJacobian is kept fixed during p consecutive iterations.One such p-cycle requires 2**p-1 solves with thefixed Jacobian. When using matrix factorization, weenvisage that the proposed inexact method wouldbe advantagoues. The inexact method is shownto be p-step convergent with Q-factor 2**p understandard assumptions. The method thus mimics theconvergence rate of a classical Newton method. Wecontrast the method to a simplified Newton method,

where it is known that a cycle of 2**p-1 iterationsgives the same type of convergence. We present somenumerical results and also discuss how this methodmight be used in the context of interior methods forlinear and nonlinear programming.

2. Local behavior of an augmentedLagrangian method for degeneratenonlinear programming

Damian Fernandez, FaMAF - Universidad Nacional

de Cordoba, Medina Allende s/n, Ciudad Universitaria,

Argentina, dfernandez@famaf.unc.edu.ar / Co-author:

Mikhail Solodov

It is known that when the penalty parameter isvery large, the subproblem associated with theminimization of the augmented Lagrangian maybe very difficult. The necessity of maintainingbounded penalty parameter is controversial, be-cause ill-conditioning disappears with a suitabledecomposition of the subproblem. In this work wepropose that the penalty parameter should takevalues inversely proportional to an error boundfunction associated to the KKT system. We obtainlocal quadratic convergence for both, primal andprimal-dual sequence, taking into account possibledegeneracy of the constraints.

3. A Krylov-based interior-pointmethod for large-scale nonconvex opti-mization

Joshua Griffin, SAS Institute Inc., 100 SAS Campus

Drive, USA, Joshua.Griffin@sas.com / Co-authors:

Ioannis Akrotirianakis, Wenwen Zhou

This talk presents a new Krylov-based interior-pointsolver developed at SAS for large-scale nonlinearnonconvex optimization. The solver combines recentresearch on (1) a primal-dual augmented Lagrangianmerit function by Gill and Robinson (2009), (2)preconditioning strategies for augmented systemsby Forsgren et al. (2007), and (3) a successivesubspace CG-type trust-region algorithm by Erwayet al. (2007). The merit function is attractive foran iterative approach because the penalty parameteris often bounded; further, the perturbed regularizedKKT system of equations are consistent with anapproximate Newton system (modulo block linearalgebra) for this merit function. Hence, the difficultyof detecting the inertia of a KKT system using onlymatrix-vector products is reduced to estimating

46 TECHNICAL SESSIONS — WEDNESDAY

the smallest eigenvalue of the corresponding aug-mented system; thus we can apply preconditionedKrylov-based strategies capable of simultaneouslysolving linear systems while estimating minimumeigenvalues to handle nonconvexity and singularitiesin the Newton equations.

� WC03Room H006 - Wednesday 15:30–17:00

Engineering Optimization IIContributed sessionChair: Rasmus Bokrantz

1. Decomposition strategy for thestochastic pooling problem

Xiang Li, Massachusetts Institute of Technology, 77

Massachusetts Ave., Building 66-363, Cambridge, MA

02139, USA, xiangli@mit.edu / Co-authors: Asgeir

Tomasgard, Paul Barton

The stochastic pooling problem is a type of stochas-tic mixed-integer bilinear program arising in theintegrated design and operation of various importantindustrial networks. This paper presents a rigorousdecomposition method for the stochastic poolingproblem. In this method, the problem is relaxed intoa lower bounding problem, which is then decomposedinto a sequence of relaxed master problems and pri-mal bounding problems. Solutions of the relaxedmaster problems yield a sequence of nondecreasinglower bounds on the optimal objective value andthey also generate a sequence of integer realizations,defining the primal problems which yield a sequenceof nonincreasing upper bounds on the optimal objec-tive value. The decomposition algorithm terminatesfinitely with an ε-optimal solution or an indicationof infeasibility of the problem. The case studyresults demonstrate the dramatic computationaladvantages of the decomposition method over botha state-of-the-art branch-and-reduce global opti-mization method and explicit enumeration of integerrealizations, particularly for large-scale problems.

2. Analyzing the competitiveness of achain of bookstores in the marketplaceby mathematical programming tech-niques

Alexander Belenky, State University-Higher School

of Economics, Moscow, Russia and Center for Engi-

neering Systems Fundamentals, Massachusetts Institute

of Technology, Cambridge, Massachusetts, USA, be-

lenky alexander@yahoo.com / Co-author: Nadezhda I.

Mikhaylova

We consider a chain of bookstores competingwith similar chains and individual bookstores in ametropolitan area, as well as with Internet retailersselling books, e-books, CDs, video- and audio-production. All the participants of the market targeta part of the same population residing in the areaand interested in buying these types of products.We formulate a problem of estimating a chain’sfair share of the market, along with its potentialto increase this share, as a two-person game inwhich the chain competes against its surrounding.In this game, both players choose their strategiesfrom a polyhedron formed by a system of linearconstraints with respect to two vector variables, andthe payoff function is a sum of two linear functionsof these (connected) variables. Finding equilibriumstrategies in the (solvable) game is reducible tosolving either quadratic optimization problems (forconstraints-equalities) or quadratic programmingones (for constraints-equalities).

3. An on-line convex hull algorithmfor approximating higher dimensionalPareto sets with applications to radia-tion therapy

Rasmus Bokrantz, Royal Institute of Technology

(KTH), RaySearch Laboratories, Lindstedtsvagen 25,

Sweden, bokrantz@kth.se / Co-author: Anders Forsgren

Multi-criteria optimization has emerged as anapproach to facilitate decision making with respectto conflicting treatment goals in radiation therapytreatment planning. Viable treatment options mayin this setting be examined by forming convexcombinations of pre-computed treatment plans. Weconsider a technique which aims to span possibletreatment options by generating treatment plansuntil the convex hull of these plans approximatesthe Pareto set sufficiently well. An upper boundon the approximation error is obtained by “sand-wiching” the Pareto set between an inner and outerapproximation. This technique requires higher di-mensional convex hulling, whose high computationalcost has hampered its application to the full rangeof problem dimensions encountered in treatmentplanning. We propose an incremental update of

TECHNICAL SESSIONS — THURSDAY 47

the convex hull that exploits problem structure andleads to a reduction in computational complexity.We discuss the benefits and limitations of the sand-wich algorithm in view of the proposed enhancement.

� WC04Room H104 - Wednesday 15:30–17:00

Nonsmooth OptimizationContributed sessionChair: Abderrahim Jourani

1. A continuous framework for open pitmine planning

Nikolai Strogies, Humboldt Universitat zu Berlin, Ger-

many, strogies@mathematik.hu-berlin.de / Co-authors:

Felipe Alvarez, Jorge Amaya, Andreas Griewank

We propose a new mathematical framework for openpit mine planning problem based on continuous func-tional analysis. Instead of the usual discrete blockmodels we apply a continuous approach that allowsfor a refined imposition of slope constraints associ-ated with geotechnical stability. The framework isposed in the function space of real-valued Lipschitzfunctions on a bounded domain. We give existenceresults and investigate qualitative properties of thesolutions.

2. Weak regularity and error bound

Abderrahim Jourani, Universite de Bourgogne, Dijon,

France, jourani@u-bourgogne.fr

The aim of the talk is to study the concept ofweak regularity introduced in A. Jourani, “Weakregularity of functions and sets in Asplund spaces”,Nonlinear Analysis Theory Methods and Appli-cations, 65 (2006), 660-676. <http://math.u-bourgogne.fr/IMB/jourani/nonlin-juillet.pdf>. Theresults obtained are used to obtain sufficient condi-tions for error bound for nonconvex systems.

THURSDAY

� ThA01Room H004 - Thursday 10:30–12:00

Algorithms for Convex Opti-mizationContributed sessionChair: Alice Chiche

1. Alternating proximal algorithmswith costs-to-move, application to do-main decomposition for PDE’s.

Pierre Frankel, Universite Montpellier 2, Residence le

Tiepolo appart B18, 115 route d’Uzes, 30 000 Nımes,

France, p.frankel30@orange.fr / Co-authors: Hedy

Attouch, Alexandre Cabot, Juan Peypouquet

We study some alternating proximal algorithms withcosts-to-move introduced by Attouch, Redont andSoubeyran. We prove that the sequences generatedby the algorithms weakly converge toward a solutionof a minimization problem or a minimization prob-lem with constraints. Applications are given in thearea of domain decomposition for PDE’s.

2. Approximate level method

Peter Richtarik, University of Edinburgh, 6317 JCMB,

Kings Buildings, EH93JZ, Edinburgh, United Kingdom,

peter.richtarik@ed.ac.uk

In this paper we propose and analyze a variant of thelevel method, which is an algorithm for minimizingnonsmooth convex functions. The main work periteration is spent on 1) minimizing a piecewise-linearmodel of the objective function and on 2) projectingonto the intersection of the feasible region and apolyhedron arising as a level set of the model. Weshow that by replacing exact computations in bothcases by approximate computations, in relative scale,the theoretical iteration complexity increases only bythe factor of four. This means that while spendingless work on the subproblems, we are able to retainthe good theoretical properties of the level method.

3. How the augmented Lagrangian al-gorithm deals with an infeasible convexquadratic optimization problem

Alice Chiche, EDF&INRIA, 1 avenue du General

de Gaulle, 92141 Clamart Cedex, France, al-

icechiche@gmail.com/ Co-author: Jean-Charles Gilbert

48 TECHNICAL SESSIONS — THURSDAY

The behavior of the augmented Lagrangian algo-rithm on an infeasible convex quadratic optimizationproblem is analyzed. It is shown that the algorithmfinds a point that satisfies the shifted constraintswith the smallest possible shift in the sense ofthe Euclidean norm and that it minimizes theobjective on the corresponding shifted constrainedset. The convergence to such a point is realized ata global linear rate, which depends explicitely onthe augmentation parameter. This suggests us arule for determining the augmentation parameter tocontrol the speed of convergence of the shifted con-straint norm to zero; this rule has the advantage ofgenerating bounded augmentation parameters evenwhen the problem is infeasible. As a by-product,the algorithm computes the smallest translationin the Euclidean norm that makes the constraintsfeasible. Implications on an SQP algorithm usingthe AL algorithm for solving its osculating quadraticproblems are discussed.

� ThA02Room H005 - Thursday 10:30–12:00

Nonlinear Programming Algo-rithms IIIContributed sessionChair: Daniel Robinson

1. Metric regularity of Newton’s itera-tion

Francisco Javier Aragon Artacho, Universidad de Al-

icante, Carretera San Vicente s/n, C.P. 03080, Spain,

francisco.aragon@ua.es / Co-author: Asen Dontchev,

Michael Gaydu, Michel Geoffroy, Vladimir Veliov

For a version of Newton’s method applied to gen-eralized equations with a parameter, we extend theparadigm of the Lyusternik-Graves theorem to theframework of a mapping acting from the pair “param-eter - starting point” to the set of all associated con-vergent Newton’s sequences. Under ample parame-terization, the metric regularity of the mapping asso-ciated with convergent Newton’s sequences becomesequivalent to the metric regularity of the generalizedequation mapping.

2. New weak constraint qualificationsassociated to the convergence of anaugmented Lagrangian method

Gabriel Haeser, University of Sao Paulo, R do Matao,

1010, Cidade universitaria, Sao Paulo, SP, Brazil,

ghaeser@gmail.com / Co-authors: Roberto Andreani,

Maria Laura Schuverdt, Paulo J.S. Silva

In this work we introduce the relaxed-CPLD con-straint qualification. This reformulation is based onthe relaxed constant rank condition of Minchenkoand Stakhovski that requires only verification ofconstant rank on subsets consisting of all equalityconstraint gradients and every inequality constraintgradient. The relaxed-CPLD condition is weakerthan Mangasarian-Fromovitz, Constant Rank, Re-laxed Constant Rank and CPLD. We also prove thatrelaxed-CPLD is still a practical constraint qualifi-cation, since we can prove convergence of an Aug-mented Lagrangian method to KKT points under thiscondition. We also introduce an even weaker and alsopractical constraint qualification.

3. Overcoming degeneracy in interior-point methods for quadratic program-ming

Daniel Robinson, University of Oxford, Mathematical

Institute, 24-29 St Giles, Oxford OX1 3LB, United King-

dom, daniel.p.robinson@gmail.com / Co-authors: Nick

Gould, Dominique Orban

We examine improved path following interior-pointmethods for quadratic programming. Taylor approx-imations and extrapolation are two well-known tech-niques for approximating the so-called central pathof barrier minimizers. The seminal work by Fiaccoand McCormick describes both of these methods un-der a non-degeneracy assumption and their effective-ness is established. During this talk, we focus onTaylor-like and associated extrapolation methods forapproximating the central path that are accurate inboth the non-degenerate and degenerate cases. Ournew method allows us to obtain substantially moreaccurate solutions than is typically possible in the de-generate case. This extra accuracy allows improvedoptimal active-set identification, which is particularlyimportant for so-called quadratic crossover methods;a quadratic cross-over method uses the solution ofan interior point phase to predict the optimal activeconstraints during the second active set phase.

TECHNICAL SESSIONS — THURSDAY 49

� ThA03Room H006 - Thursday 10:30–12:00

Engineering Optimization IIIContributed sessionChair: Marıa Agustina Reinheimer

1. An optimization modeling andalgorithmic framework for real-time es-timation of dynamic origin-destinationtrip matrices

Lidia Montero, Universitat Politecnica de Catalunya,

C/JordiGirona 1-3 C5217, 08034 Barcelona, Spain,

lidia.montero@upc.edu / Co-authors: Jaume Barcelo,

Laura Marques, Carlos Carmona

From the point of view of the transportation com-munity, the dynamic estimates of OD trip matricesis a major input to dynamic traffic models used forestimating the current traffic state and forecastingits short term evolution. New technologies havemade possible to consider new formulations of thedynamics models involved. Space-state models fordynamic systems comprise transition equations thatcapture the evolution of the state variables (originto destination flows) over time and measurementequations that capture the mapping of the statevariables on the direct measurements of vehiclecounts using travel time distributions provided bynew technologies. In this work, Kalman filtering isconsidered as an incremental algorithm to solve aleast-square problem. The use of a least-square ap-proach to solve the dynamic OD estimation problemis proposed by exploiting a space-state formulationdescribed in Barcelo et al (2010) and deriving aLSQR algorithm, accounting for problem’s sparsity.

2. Stochastic optimization of hybridsystem with activation delay and exe-cution lag

Giovanni Granato, ENSTA ParisTech - INRIA, 8, rue

Raymond Marcheron, Chez M VIANA, 92170 Vanves,

France, giovanni.granato@ensta.fr

We are interested in analyzing optimal controlproblems of hybrid dynamical systems that containsan execution lag and an activation delay. Weconsider that the controller may choose to executea transition between several continuous dynamicsthrough a discrete, time punctual order. The contin-uous dynamics depends on a parameter containingan incertitude, of know probability distribution.

Transition orders are subject to an execution lag,which means that it executes only after some time.In addition, we consider that a time delay separatetwo consecutive. We derive a stochastic dynamicprogramming principle verified by the value functionof an associate finite time optimal control problem.Moreover, propose an optimal trajectory reconstruc-tion method. Finally, we present some numericalresults for an industrial application, namely, theoptimization of energy management for hybridvehicles.

3. Dynamic mathematical model tooptimize the cooling process in hardcandies

Marıa Agustina Reinheimer, INGAR - CONICET

- UTN, Avellaneda 3657, Santa Fe (3000), Argentina,

mareinheimer@santafe-conicet.gov.ar / Co-authors:

Sergio Mussati, Nicolas Scenna

This paper presents a mathematical model to deter-mine optimal operating policies of the cooling processaiming to prevent product defects. From the qualitypoint of view, previous simulation results showedthat cooling air flow velocities, residence time in thecooling equiptment and the thermal conductivity ofproduct have a strong influence on the number ofdecomised products as non-conforming. Certainly,high air velocities, especially at the beginning ofthe process, increase the product fragility for thewrapping stage. The most practical way of avoidingmisshapen candies is by minimizing the differenceof temperature between the centre and the surfaceon candy. Therefore, an optimization mathematicalmodel is developed to determine the best operatingpolicies which minimize the temperature differenceduring the cooling process. The resulting modelis discretized using a second-order centered finite-difference method. GAMS modeling tool is used forits implementation. Numerical results are discussedthrough different study cases.

� ThA04Room H104 - Thursday 10:30–12:00

Vector Optimization with Appli-cations IInvited sessionOrganizer/Chair: Fabian Flores-Bazan

50 TECHNICAL SESSIONS — THURSDAY

1. Well-posedness of quasi C-convexvector optimization problems

Giovanni Paolo Crespi, University of Valle d’Aosta,

Loc. Grand Chemin 73/5, Italy, g.crespi@univda.it /

Co-authors: Matteo Rocca, Melani Papalia

Well-posedness of a scalar minimization problemis a classical notion and plays a crucial role in thestability theory for optimization problems. Thenotion of well-posedness for vector valued problemsis less developed. However some definitions havebeen proposed for vector minimization problems (seee.g. the survey by P. Loridan in 1995) and somecomparisons have been made among these definitionsand with their scalar counterparts. In a previouspaper we introduced a quite strict notion of well-posedness and compared it to well-posedness in thestrongly extended sense, as introduced by Huang in2000. In this research, we investigate well-posednessproperties of vector optimization problems withC-convex and quasi C-convex objective functionsas a generalization of results which hold for thescalar case. The main result involves also someinvestigation on stability properties of vector quasiC-convex optimization problems.

2. Dynamic model for planning andmultiobjective optimization of aggre-gate production

Marcos Flores Chavez, Universidad Tecnica de Oruro,

Facultad Nacional de Ingeniera Ingenierıa de Sistemas

– Informatica, Oruro, Bolivia, m.flores.ch@gmail.com

/ Co-authors: Edgar Pinto Landaeta, Reynaldo Mita

Laura

Organizations are on the way to assume that thecost, quality and time are the most important goalsin the production planning process. In order toachieve these multiple objectives and to attain thedesired end purpose, multiobjective programmingmodels allow to develop and analyze the system ina more complete and complex form, as one can alsofind multiple sub-goals within an organization. Theproduction manager must allocate optimally all theresources available. When analyzing a system, onecan evaluate its behavior using a simulation modelbased on the methodology of system dynamicsthrough cause / effect Forrester diagrams (JayForrester creator of the methodology and one of thehonorees Operations Research from INFORMS),through which one can make decisions for a better

development of the system in general, and applymore precise and specific methodologies in solvingthe identified problem. The work is based primarilyon the creation of a mixed aggregate planning modelunder multi-objective analysis and system dynamics,which is based on the theory of decision making,linear programming, aggregate planning, systemsapproach.

� ThB01Room H004 - Thursday 13:30–15:00

Convex & Nonsmooth AnalysisContributed sessionChair: Dariusz Zagrodny

1. Variational convergence of bivariatefunctions: Saddle functions-an update

Quoc Khanh Phan, International University of

Hochiminh City, Department of Mathematics, UC Davis,

1 Shields Avenue, Davis, CA 95616, USA, pqkhan-

hus@gmail.com Co-authors: Alejandro Jofre, Roger J-B

Wets

Partially motivated by the insights gained fromour study of lopsided convergence, the notionepi/hypo-convergence for bivariate functions isrevisited so that one can apply it directly to finitevalued bivariate functions defined on the product oftwo sets. In the process some new concepts, suchas tightness and ancillary tightness, are introducedthat allows us to arrive more immediately to theproperties required in the applications of the theory.The accent is placed on a framework that leadsto unique limits rather than limits that had to bedefined in terms of equivalence classes. Also therelationship with lopsided convergence is clarified.

2. An axiomatic approach of gap func-tion for quasivariational inequalities:Error bound and application to Nashequilibrium

Matthieu Marechal, PROMES CNRS UPR 852,

Tecnosud Rambla de la Thermodynamique, 66100

Perpignan, France, mathieu.marechal@univ-perp.fr /

Co-authors: Didier Aussel, Rafael Correa

Gap function (or merit function) is a classical toolto reformulate a variational inequality problem intoan optimization problem. During this conference Iwill show how we can adapt this technique to qua-

TECHNICAL SESSIONS — THURSDAY 51

sivariarional inequalities, that is to say, variationalinequalities in which the constraint set dependson the current point. Following Fukushima [1],an axiomatic approach is proposed. Error boundsfor quasivariational inequalities are provided andan application to generalized Nash equilibriumproblems is also considered.

References:

[1] Fukushima, M., A Class of Gap Functions for

Quasi-Variational Inequality Problems, J. Ind. Manag.

Optim. 3 (2007), no. 2, 165–171.

[2] Marechal, M., Gap functions for quasivariational

inequalties and generalized Nash equilibrium problems,

submitted, 2010, 17 pp.

3. Vector variational principles

Dariusz Zagrodny, Cardinal Stefan Wyszynski

University, 01-815 Warszawa, Dewajtis 5, Poland,

d.zagrodny@uksw.edu.pl

Let K ⊂ Y be a closed convex cone, D ⊂ K be aclosed convex subset of K such that 0 6∈ cl (D + K)and let f : X −→ Y be a mapping defined on acomplete metric space (X, d). The aim of the talk isto present two vector variational principles:

1: there is x ∈ X such that for all z ∈ X \ {x}

“f(x)−K

”∩“f(z) + d(z, x)D

”= ∅;

2: for any (λi)∞i=0 ⊂ (0, 1) with∑∞

i=1 λi <∞ thereare x ∈ X, a sequence (xi)∞i=0 ⊂ X with xi → xand d ∈ D such that for all z ∈ X \ {x}

“f(z)+

∞Xi=0

λi‖z−xi‖2D”∩“f(x)+

∞Xi=0

λi‖x−xi‖2d−K”

=∅

[1] E.M. Bednarczuk, D. Zagrodny, Vector variational

principle, Archiv der Mathematik, 93 (2009), 577-586.

[2] E.M. Bednarczuk, D. Zagrodny, A smooth vector vari-

ational principle , SIAM J. Control Optim. 48 (2010),

3735-3745.

[3] J.M. Borwein, D.Preiss, A smooth variational principle

with applications to subdifferentiability and to differentia-

bility of convex functions, Trans. Amer. Math. Soc. 303

(1987), 517-527.

[4] I. Ekeland, On the variational principle, J. Math.

Anal. Appl., 47 (1974), 324–353.

� ThB03Room H006 - Thursday 13:30–15:00

Engineering Optimization IVContributed sessionChair: Vincent Malmedy

1. Discrete adjoint techniques forflow optimization and POD supportedshape optimization

Rolf Roth, TU Darmstadt, Bismarckstrasse 63a,

64293 Darmstadt, Germany, rroth@mathematik.tu-

darmstadt.de / Co-authors: Jane Elsemuller, Stefan Ul-

brich

We describe a systematic way to generate adjointcode by applying an efficient sparsity exploiting for-ward mode of Automatic Differentiation to the orig-inal code. The result is a linear system for the ad-joint, that can be solved by taking advantage of theoriginal code and reusing the existing (parallel) struc-ture for multicore, multigrid and AD. This procedurehas been applied to the finite volume, parallel, block-structured, multigrid flow solver FASTEST, whichcan also run Large Eddy Simulations and is writtenin Fortran. As usual in adjoint AD approaches, ob-taining the state is cheaper than the adjoint. We tryto reduce the cost for an optimization with the usageof a POD model in the flavour of RMTR and TR-POD. Numerical results for an engineering applica-tion using LES and preliminary results for the PODapproach involving shape optimization will be pre-sented.

2. Sparsity-regularized photon-limitedimaging

Roummel Marcia, University of California-Merced,

5400 North Lake Road, Merced CA 95343, USA, rmar-

cia@ucmerced.edu

In many medical imaging applications (e.g., SPECT,PET), the data are a count of the number of pho-tons incident on a detector array. When the num-ber of photons is small, the measurement processis best modeled with a Poisson distribution. Theproblem addressed in this talk is the estimation ofan underlying intensity from photon-limited projec-tions where the intensity admits a sparse or low-complexity representation. This approach is based onrecent inroads in sparse reconstruction methods in-spired by compressed sensing. However, unlike mostrecent advances in this area, the optimization for-

52 TECHNICAL SESSIONS — THURSDAY

mulation we explore uses a penalized negative Pois-son log-likelihood objective function with nonnega-tivity constraints (since Poisson intensities are nat-urally nonnegative). This talk describes computa-tional methods for solving the nonnegatively con-strained sparse Poisson inverse problem. In partic-ular, the proposed approach incorporates key ideasof using separable quadratic approximations to theobjective function at each iteration and penalizationterms related to l1-norms of coefficient vectors, totalvariation seminorms, and partition-based multiscaleestimation methods.

3. Modelization of snakeskins pigmen-tation patterns through multilevel op-timization

Vincent Malmedy, University of Namur (FUNDP),

Rempart de la Vierge 8, B-5000 Namur, Belgium, vin-

cent.malmedy@fundp.ac.be / Co-authors: Andre Fuzfa,

Philippe L. Toint

In this talk, we present an application of multileveloptimization methods to the modelization of snake-skins pigmentation patterns by a cell-chemotaxismodel posed on curved geometric domains and de-scribed by nonlinear PDEs. More specifically, we dis-cuss the discretization of the problem on curved do-mains and its formulation as a least-square problem.We then consider the resolution of this nonlinear opti-mization problem by the Recursive Multilevel Trust-Region (RMTR) method of Gratton, Mouffe, Tointand Weber-Mendonca (2008), to take advantage ofthe potentially many levels of discretization. In ad-dition to mesh-refinement technique, this method usethe problem multilevel hierarchy to determine trust-region steps by minimizing the problem at a coarserlevel, the algorithm being able to switch cleverly be-tween these particular steps and the classical stepsarising from the minimization of the quadratic Tay-lor’s model inside the trust-region. Numerical resultsare presented and analyzed.

� ThB04Room H104 - Thursday 13:30–15:00

Vector Optimization with Appli-cations IIInvited sessionOrganizer/Chair: Fabian Flores-Bazan

1. Non- negativity of information valuein quadratic games

Sigifredo Laengle, Universidad de Chile, Diago-

nal Praguay 257, Of.1302A, Santiago, Chile, slaen-

gle@fen.uchile.cl / Co-author: Fabian Flores-Bazan

In the context of optimization problems of an agent,“having more information without additional cost isalways beneficial” is a classic result by D. Blackwell(1953). Nevertheless, in the case of strategic interac-tion this is not always true. Under what conditionsmore information is (socially) beneficial in games?How the characteristics of the players and the in-teraction among them affect the information value?Existing literature varies between two ends: on theone hand, we find works that calculate the informa-tion value of particular cases not always easy to gen-eralize; on the other hand, there are also abstractstudies which make difficult the analysis of moreconcrete applications. In order to fill this gap, wecalculated the information value in the general caseof constrained quadratic games in the framework ofHilbert spaces; we determined the conditions to as-sure its non-negativity; studied how characteristics ofthe players affect their value. This work presents themost important results, a discussion of them and arevision of the posible applications. As a result of ourwork we found a close relationship between the sym-metry of information and the mathematical propertyof invariance (subspaces). Such property is the basisto calculate the information value and demonstratingits non-negativity. Otherwise, we found how the in-formation value depends or not of some players char-acteristics. Such results improve the understandingof general conditions that assure the non-negativityof information value. In the immediate thing, thiswork can be extended to the study of other payofffunctions with more general constraints.

2. Efficiency, weak efficiency andproper efficiency in multiobjective op-timization

Felipe Lara-Obreque, Universidad de Concepcion,

TECHNICAL SESSIONS — THURSDAY 53

Chile, felipelara@udec.cl / Co-author: Fabian Flores-

Bazan

The linear scalarization procedure has proved to bevery important in multiobjective optimization. Inthis talk we establish a series of estimates for the(weak, proper) efficient solution sets as well as forits assymtotic cone, for a class of nonconvex multi-objective functions. Several results in the literatureare refined and extended, in particular, a character-ization for the nonemptiness and boundeness of theproper efficient solution set is revisited.

3. Equivalent formulations to Gordanalternative theorems and its uses invector optimization

Fabian Flores-Bazan, Universidad de Concepcion, De-

partamento de Ingenierıa Matematica, Avda Esteban

Iturra S/N, Concepcion, Chile, fflores@ing-mat.udec.cl

We establish general equivalent formulations toGordan-type alternative theorems involving convexcones with possibly empty interior. This will be ap-plied to characterize properly/weakly efficient solu-tions through linear scalarization, as well as to char-acterize the Fritz-John type optimality conditions.The two-dimensional setting allows us to get opti-mality of our results, showing convexity is present.Some the results were obtained with Fernando Flores-Bazan and Cristian Vera from Universidad Catolicade la Santısima de Concepcion.

Author Index

AUTHOR INDEX 55

AAgarwal, Anshul, TB02Aguilar, Jose, WA04Aguirre, Pio, MA02Akrotirianakis, Ioannis, WC02Alasino, Noelia, MA02Albornoz, Vıctor M., TA03, (TA03)

Ali Khan, M., MC04, TB03Alvarez, Felipe, TA01, WC04, (MC01, TA01, ThP)

Alzalg, Baha, MC03Amaya, Jorge, WC04Andreani, Roberto, ThA02Andrieu, Laetitia, WA03, (WA03)

Aragon-Artacho, Francisco J., ThA02Aronna, M. Soledad, MC02Arouxet, Marıa Belen, WA02Attouch, Hedy, TA0, ThA01Aussel, Didier, ThB01

BBandoni, J. Alberto, MA02Barcelo, Jaume, ThA03Barton, Paul, WC03Barty, Kengy, WA03Behling, Roger, TC02Belenky, Alexander, WB03, WC03Benz, Sonia, MB02Biegler, Lorenz T., TB02, (MA02, TB02)

Blanco, Anıbal M., MA02Bokrantz, Rasmus, WC03, (WC03)

Bonnans, Joseph F., MC02, TC04, (MC02, ThSP2)

Bonnisseau, Jean-Marc, MC04, (MC04)

Borzi, Alfio, TC01Brandenburg, Christian, TC01Bravo, Fernanda, TB03Brunet, Robert, MB02Bruno, Sergio, MC03, (MC03)

CCaballero, Jose A., MB02Cabot, Alexandre, ThA01Canales, Cristian M., TA03Cardona, Daiver, MA04Carmona, Carlos, ThA03Carrasco, Miguel, MC01Carvajal, Andres, TC04, (TC04)

Castagne, Michel, WB02Cen, Zhihao, TC04Cervinka, Michal, TB01

Chaudoye, Fabien, WB02Chen, Xiaojun, WSP2Chiche, Alice, ThA01, (ThA01)

Christel, Thibault, TC04Codina, Esteve, WB03, (WB03)

Cominetti, Roberto, WPConca, Carlos, TC01Conejeros, Raul, TC03, (TC03)

Correa, Rafael, ThB01, (WSP2)

Crespi, Giovanni P., ThA04, (ThB04)

Crespo, Fernando, WA01Curtis, Frank E., TC02 (TC02)

Custodio, Ana Luisa, WA04Czarnecki, Marc-Olivier, TA01

Dda Veiga, Sebastien, WB02de Lara, Michel, TA03, TB03de Prada, Cesar , MA02Delbos, Frederic, WA02Dentcheva, Darinka, MSP2Deride, Julio, MC04Dıaz, Juan, TA04Dıaz, Marıa Soledad, TB02Dmitruk, Andrei, MC02Dontchev, Asen, ThA02Dorsch, D., TB01Duran, Guillermo, TB03

EEchebest, Nelida, WA02Eckstein, Jonathan, TA01, (TSP2)

Egea, Jose, TB02Ekeland, Ivar, TA03Elsemuller, Jane, ThB03Escobar, Juan, TB04Espinoza, Daniel, WA01

FFernandez, Damian, WC02Figueroa, Nicolas, WA01Fischer, Andreas, TC02Flores, Salvador, WB04Flores-Bazan, Fabian, ThB04, (ThA04, WSP1)

Flores-Chavez, Marcos, ThA04Font, Gregory, WB02Forsgren, Anders, WC02, WC03Franco, Alejandro, TC03Frankel, Pierre, ThA01

56 AUTHOR INDEX

Freund, Robert, WC01Fuentes, Matıas, MB04Fujisawa, Katsuki, MB03Fukuda, Mituhiro, MB03, (MB03)

Fuzfa, Andre, ThB03

GGajardo, Pedro, TB03, (TB03)

Gallivan, Kyle, MC01Garces, Rodrigo, MB03Garcıa, Julio, WB03Gaydu, Michael, ThA02Geoffroy, Michel, ThA02Gilbert, Jean Charles, ThA01Girardeau, Pierre, WA03Godoy, Ezequiel, MB02Gomez, Walter, MB03Gondzio, Jacek, MA03, (MA03)

Gonzalez Andrade, Sergio, TC01, (TC01)

Gonzalez-Brevis, Pablo, MA03Gould, Nick, ThA02Granato, Giovanni, ThA03Gratton, Serge, WA02, WB02Griewank, Andreas, WC04Griffin, Joshua, WC02, (WC02)

Grossmann, Ignacio E., MP, TA02, (MB02, TA02)

Guigues, Vincent, MC03Guillen-Gosalbez, Gonzalo, MB02Gutierrez, Gloria, MA02

HIJKHaeser, Gabriel, ThA02Hare, Warren, MA01, (MA01)

Henrion, Rene, TSP1Herrera, Eddy, TC03, WB03Herves, Carlos, MB04, (MB04)

Hoai, An Le Thi, WB04Hoch, Patricia, TB02Ivorra, Benjamin, MC01Jarre, Florian, MB03, WB01, (WB01)

Jarusek, Jiri, TB01Jimenez, Laureano, MB02Jofre, Alejandro, MC04, TC04, ThB01, (MP)

Jongen, H. Th., TB01Jourani, Abderrahim, WC04Khanh, Quoc Phan, ThB01Kumar, Mukesh, TA04

LLaengle, Sigifredo, ThB04Laiglecia, Juan Ignacio, TB02Laloyaux, Patrick, WB02, (WB02)

Langouet, Hoel, WB02Lara-Obreque, Felipe, ThB04Lecaros, Rodrigo, MC01Lewis, Adrian, MA01L’Huillier, Gaston, WA01Li, Xiang, WC03Lisboa, Adriano, WA04Liu, Jia, MA04Locatelli, Marco, WSP1Lopez, Julio, TA01, WB01Lopez, Ruben, WB01Lotito, Pablo, MC02Luo, Zhi Quan, MSP1, MB01

MMacconi, Maria, TC02Magand, Sebastien, WB02Mahadevan, Rajesh, TC01Malmedy, Vincent, ThB03, (ThB03)

Marcia, Roummel, ThB03Marechal, Matthieu, ThB01Marques, Laura, ThA03Martinet, Vincent, TB03Martınez, Francisco, MB04Martınez, Jose M., MC01Matallana, Luis G., MA02Matonoha, Ctirad, TB01McLennan, Andrew, TB04Men, Abby H., WC01Mifflin, Robert, MA01Mikhaylova, Nadezhda I., WC03Miranda, Jaime, WA01Mita, Reynaldo, ThA04Moazeni, Somayeh, MA04, (MA04)

Mohan, Raj Singh, TC03Monteiro, Paulo K., TB04, (TB04)

Monteiro, Renato, MB01Montero, Lidia, ThA03Mordukhovich, Boris, MB04Mores, Patricia, MB02Morini, Benedetta, TC02Moroni, Sofıa, TC04Munari, Pedro, MA03Muramatsu, Masakazu, MB03Mussati, Miguel, MA02, MB02, ThA03

AUTHOR INDEX 57

NNakata, Maho, MB03Narayanan, Hariharan, WC01Navia, Daniel, MA02Nedich, Angelia, MB01, (MB01)

Nguenamadji, Orntangar, MC04Nguyen, N.C., WC01Nocedal, Jorge, ThSP1

OObregon, Nelson, TC03Ocana, Eladio, TA03Oliveros-Ramos, Ricardo, TA03Orban, Dominique, ThA02Ordonez, Fernando, (ThSP1)

Outrata, Jiri , TB01, WB01, (TB01)

PPapalia, Melani, ThA04Pareja, Claudio, TA03Parrilo, Pablo, WC01Peraire, Jaime, WC01Perez-Correa, Jose Ricardo, MB02, TB02Peypouquet, Juan, TA01, ThA01Piazza, Adriana, MC04, TB03Pilotta, Elvio, WA02Pinto Landaeta, Edgar, ThA04Porcelli, Margherita, TC02

RRaghunathan, Arvind, TA02Ramırez, Hector, TA01, TB03, WB01Ramos, Angel Manuel, MC01Rawal, Nekram, TC03Reinheimer, Marıa Agustina, ThA03, (ThA03)

Repetto, Andrea, TC04Richtarik, Peter, ThA01Rivera, Jorge, MB04, TA04Robinson, Daniel, ThA02, (ThA02)

Rocca, Matteo, ThA04Rodrıguez, Marıa Analıa, TA02Rodriguez, Mariela, TB02Romisch, Werner, MC03Rostek, Marzena, TC04Roth, Rolf, ThB03Ruszczynski, Andrzej, MC02

SSaldanha, Rodney, WA04Sagastizabal, Claudia, MC03Sanz, Leon, TC01Sarabia, Daniel, MA02Sartenaer, Annick, WB02Scenna, Nicolas, MA02, MB02, ThA03Schobel, Anita, WB04Scholz, Daniel, WB04, (WB04)

Schuverdt, Maria Laura, ThA02Scott, Felipe, TC03Shapiro, Alexander, (WP)

Shikhman, Vladimir, TB01Silva, Francisco, MC02Silva, Paulo J.S., MC01, TA01, ThA02Sinoquet, Delphine, WB02Solodov, Mikhail, TSP2, WC02Stara, Jana, TB01Strogies, Nikolai, WC04Sumaila, Rashid, TA03

TTam, Jorge, TA03Terlaky, Tamas, MA03, (MSP1)

Toikka, Juuso, TB04Toint, Philippe L., ThP, WA02, ThB03Tomasgard, Asgeir, WC03Tourky, Rabee, TB04Triossi, Matteo, TB04Troeltzsch, Anke, WA02, (WA02)

Truong, Bao, MB04Tshimanga, Jean, WB02

UVUlbrich, Stefan, ThSP2, TC01, ThB03Vaishya, R.C., TC03Vaz, Ismael, WA04, WB04Vecchietti, Aldo, TA02Veliov, Vladimir, ThA02Vera, Jorge, WC01, (WC01, TSP1)

Vicente, Luis N., TP, WA04, WB04Vieira, Douglas, WA04, (WA04)

Vincent, Charles, TA04, (TA04)

58 AUTHOR INDEX

WZWaki, Hayato, MB03Wang, Xuefeng, MA04Weber, Richard, WA01, (WA01)

Weintraub, Andres, TB03Weretka, Marek, TC04Wets, Roger J-B., MC04, ThB01, (MSP2)

Wright, Stephen, MA01, (TP)

Zagrodny, Dariusz, ThB01, (ThB01)

Zhou, Wenwen, WC02Zhu, Donghua, MA04

Appendix

12 Metro de Santiago60

13Travel & Tour Information

SANTIAGO

The capital of Chile emerges as one of the most recommended cities for tourism and for conven-tions and business trips in South America. It has modern facilities, state of the art te-chnologies, high quality accommodation, hotels and convention centers with a capacity to lodge up to 7 thousand delegates, and has companies with high ex-perience in the events industry. An advanced deve-lopment in telecommunications permits tourists and delegates to continue being connected with their work and homes. Its tradition and history are tangible in its civic quarter (center), witness of the republican life of the country.The history, art and civic tradition are spread throughout its museums, art galleries, and artisan’s centers. The university campuses confirm its leaders-hip as a main seat of higher education in the country. In this capital, as well as in Valparaiso and Isla Negra (both at less than 100 km far from the ca-pital) tourists can have a touching approach to the life and work of Pablo Neruda, Literature Nobel Awar-ded, when visiting his museum houses. Santiago is the starting point for domestic and international flights, besides being the departure cen-ter to travel through the highways towards the North and South of the country and to different places of the Central Valley, that go from the Coast Mountain Range, passing through soils that house fertile farms with agriculture crops and vineyards that are the base of internationally renowned Chilean wine production. Santiago is also the capital of the Metropoli-tan Region, which extends in an area of 6 provinces, from the heart of the city to the mountains and va-lleys bathed by rivers that give life to enjoyment and recreation for its visitors.A must-to-see experience in the outskirts of the city of Santiago is the famous wine tour that allows tourist to visit famous vineyards located in the outskirts of the city and to visit the Cajón del Maipo or Pomaire. The first one, a place of mountains and relaxation to spend a quiet weekend or even a day, and on the other hand, Pomaire, a famous place for its pottery, ceramics and Chilean handicrafts besides the typical gastronomy such as “empanadas” or “pastel de choclo” (corn pie). Another attractive alternative is to take a tour to Valparaiso and Viña del Mar, visiting on the way a vineyard in the Casablanca Valley.

SANTIAGO CIVIC DISTRICT

This area houses all major government in-frastructure, as well as ministries, public entities and organizations, like the Presidential Palace of La Moneda; Plaza de la Constitución, with the statues of the ex-presidents of the Republic: Jorge Alessan-dri Rodríguez, Eduardo Frei Montalva and Salvador Allende Gossens; and the Plaza de la Ciudadanía (Citizenship’ Square) with the statue of the ex-Presi-dent Arturo Alessandri Palma. In the year 2006, La Moneda Cultural Center was inaugurated an underground space that has per-manent and temporary exhibitions.

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14 Travel & Tour Information

GASTRONOMY QUARTERS AND BARS

Santiago delights its visitors with a wide va-riety of bars, pubs, restaurants and discos that are waiting for the tourists to enjoy their charms and bo-hemia, with live and non-live music, wines and spirits, national liquors such as pisco sour and delicious dis-hes, fish and seafood being the most requested one. These establishments are located in neighbor-hoods such as Brasil, Lastarria, Plaza Italia, Bellavis-ta (with discos), Plaza Mulato Gil de Castro (with cultural activities), Nuñoa (with theater), Suecia (with discos), Providencia and Patio Bellavista, and in El Bosque-Isidora Goyenechea suburbs. The shopping center (mall) Parque Arauco has a terrace with many restaurants and cafés.

VALLE DEL MAIPO VINEYARDS AND WINE ROUTE

The warm to hot privileged weather, with dry summers and average temperatures of 25ºC and an annual average of 14ºC, make the Valle del Maipo a place favorable for grapevine growing that give origin to internationally renown exportation wines such as Cousiño Macul, Santa Rita, Undurraga and Concha y Toro, among others, which give life to these soils that have generously produced their fruits, capturing with their exquisite bouquet or aroma thousands of fine palates. Today, all these wineries receive tourists and show wine-making through their guided tours, which include wine tasting and the possibility to buy souve-nirs. These wine routes can be also be made through travel agencies. It is a good and healthy entertain-ment for the week ends and holidays.

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SKI CENTERS

Santiago is attractive to foreigners not only be-cause of what it offers within the city limits, but also thanks to the beauty and proximity of four of the most important ski resorts of the country. These resorts have different ski runs that with the quality of the snow and excellent infrastructure permit tourist to enjoy a spec-tacular stay especially during the months of June to October. Located in privileged places by the beauty of its landscape, where you can go skiing, snowboard and helisky (in most of them), it is also possible to enjoy the comfortable and complete infrastructure and equi-pment of the resort which offers lodging, catering, ski schools and night entertainment. Tourists can also rent ski equipment, have a good time in its pubs, bars, cafeteria, parking lots, and in case of any inconvenience it also has a medical cli-nic. Three of these ski resorts are located to the west of Santiago, an hour away by car, and after 40 km of distance you are in the Andean Mountain Range; its ski runs are interconnected, transforming the area in the widest skiing place of the Southern hemisphere.

They are:

Farellones – El Colorado

These are the most frequented ones because of the near-ness from the capital. 40 km and 45 km respectively, at 2.800 m above sea level and with an unevenness of 903 m. The area has small hotels and rental apartments.

La Parva

Located at 2.700 m height and some 50 k away from Santiago, this winter ski resort is the highest visited one for the amount of cottages and private departments designed with a beautiful mountain like architecture, to be rented for the season.

Travel & Tour Information

Valle Nevado

It is 60 km to the east of Santiago, at 2.700 m above sea level and 14 km inside Farellones. It is the most modern ski resort of all. Starting out from Farellones, at Curve 40, a paved road leads to the resort’s spec-tacular hotels with 800 hundred bed and ski instruc-tions and all kind of facilities that makes the tourists’ stay the most exciting experience.

Portillo

It is located 145 km to the Northeast of Santiago, at 2.885 m above sea level. It has a hotel with different types of accommodation and also the Octagonal and Inca Lodges. The World Ski Championship was held there in the year 1996, during which many Interna-tional records were beaten.

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PhD in Mathematics

The PhD program in Mathematics provides training suitable for employment in academics, indus-trial research and development agencies, as well as in research-oriented government agencies.

It usually takes a candidate 4 years to complete the program. The first two years are mainly devo-ted to coursework and choosing a thesis area. The student is then expected to take a Qualifying Exami-nation related to his/her thesis proposal. Thereafter, the doctoral candidate focuses on carrying out his/her research project in any of the research lines of the Department of Mathematical Engineering (DIM) and the Center for Mathematical Modeling (CMM): partial differential equations, discrete mathematics, mathematical mechanics, optimization and equilibrium, randomness, information and stochastic modeling. Students may also participate in some of the mathematical modeling research projects carried out in the DIM or CMM in fields such as mining, telecommunications, energy, forestry, genomics, information security, environmental sciences, and transportation.

A necessary condition for the successful fulfillment of the program is the submission of original re-search to a scientific journal. Proficiency in a foreign language is also required.

Students are encouraged, and have many opportunities, to arrange research visits to strong research centers and attend conferences, specialized schools, and workshops.

Our program offers the possibility of obtaining a double Ph.D. with one of several universities in France, Italy, Spain and other countries. Participants of a joint program will spend approximately one and a half years in the partner university working with a local, second advisor. At the completion of the program, the student will obtain a doctoral degree from both the University of Chile and the co-host university.

AccreditationThis program was accredited by the Graduate National Accreditation Commission (CONAP) for the maximum period, until June 2013.

More informationProf. Salomé MartínezTelephone: (562) 9784343E-mail: pgrado@dim.uchile.cl

www.dim.uchile.cl/doctoradowww.dim.uchile.clwww.cmm.uchile.cl

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Center for Mathematical Modeling Universidad de Chile

The Center for Mathematical Modeling (CMM) at Universidad de Chile was established in 2000 to enhance and enlarge the scope of applications of the Mathematical Engineering Department (DIM) at the same univer-sity, where the idea of such center was already present on the 90’s. Since its creation the CMM is founded by a project FONDAP-CONICYT, and it is part of the CNRS, France, as an associated international unit, the first out of France in mathematics. The center is located at the Faculty of Physical and Mathematical Sciences, the oldest, most prestigious and productive school of engineering in Chile. As a consequence our center has a strong scientific link with several departments in this school such as: industrial, mechanical, electrical, computer science and earth science. We also have privileged access to the 4000 engineering students of the school and to more than 500 graduate students on diverse fields of science and engineering.

The mission of CMM is to create new mathematics and to use it to solve problems arising from other scien-ces, the industry or government. This is done by a team that contains a world class of leading researchers in mathematics. Indeed, if we order mathematical institutions that produce more than 500 papers in the last 10 years, by the impact of its papers, our university appear on the 60th position, being the first in Ibero-America and preceded only by the best in USA, Europe one Chinese and two from Israel. This team is complemented by a highly trained team of scientist and a good number of the best Ph.D. students in mathematics and engineering students that the country has. As it is well known applied mathematics plays a fundamental role in science and technology. In particular, engineering become very dependent of the new tools developped by applied mathematics and this will tend to increase in the years to come. Our center focuses on collaborative work between its members, applied mathema-ticians at other universities and researchers from other fields, around complex problems in engineering, biology, telecomunications to mention just a few examples. CMM also foster contacts between academia and industry, which leads to long-term research collaborations.

Scientific excellence is the first strategic objective of the center and this guides its activities. The CMM has 30 associated researchers from DIM, Universidad de Chile and 10 researchers from Universidad de Concepción. We receive every year more than 100 visitors from all over the world, mainly USA, France and other European countries as well as China and Japan. We have 56 graduate students doing their Ph.D. in applied mathematics, some of them in very concrete industrial problems. We also attend more than 206 undergraduate students in Ma-thematical Engineering, probably the most prestigious undergraduate career in our School. At least half of them pursue Ph.D. programs abroad, in the best universities in the world, and most of them return to the country to lead scientifically the departments of mathematics, economy and operation research in Chile. This is complemen-ted by our successful postdoc program. CMM is becoming an interesting place in the world for young scientists that look for a place where to start their careers in a competitive, friendly environment and well connected to applications. Every year we receive around 10 new postdocs from all over the world, mainly from Europe, China, Latin-America and USA.

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CMM has a record of success in industrial problems. One of our best partners is CODELCO, the largest co-pper enterprise in the world. We are working, jointly with researchers at CODELCO, its associated centers and start-up companies in several complex projects that are relevant in all the process of the company, ranging from bioleaching, rock blustering, fragmentation, converter processes and strategic and logistic planning. We also have worked in telecommunications with their respective Ministry in Chile, Colombia and now in Peru. In forestry we have worked with the main Chilean companies and Fundación Chile. The international essence of the center leads us naturally to develop projects worldwide. In particular, we have projects with Alstom; Siemmens; Bombardier; Hewlett-Packard; EDF, SNCF and Dassault in France. In energy, we have given technical support to the National Commission of Energy on renewal and non-conventional sources of energy and more recently on nuclear energy. We have also important projects with the Education Ministry and other state agencies. LAN Chile, Telefonica, Forestal Arauco, El Metro, Enersis, Endesa, Antofagasta Minerals are among of our best Chilean industrial partners.

Several applied research projects developed at CMM are focused on models with an underlying network structure. Depending on the application, the network may be finite or infinite, deterministic or stochastic, and the interest may be directed to understand its dynamical behaviour and/or the equilibrium states (transporta-tion, genomics and telecommunications to mention some). The mathematical analysis and the computation of solutions for these models raise the need for new concepts, theorems, algorithms and computational methods. The last issue is relevant because we are dealing with real size networks, with thousands of nodes, arcs and variables, coming from production and service sectors. The difficulty to compute solutions or to simulate beha-viors is a non-trivial problem for these models, requiring efficient algorithms and efficient implementations. The network structure plays a role in the computational aspects since it is well adapted to distributed computing by using multiple processors (ideally hundreds for our models). For that reason CMM has created a laboratory on high performance computing and we have one of the most powerful clusters in the country, which we expect to enlarge in the near future. We also participate actively on two international networks on grid computing PRIMA and GELATO, and we are the main Chilean node for them. In the country we give support to several universi-ties in this topics. Also some public agencies like the National Meteorological Service benefit from our cluster.

For further information please go to:

www.cmm.uchile.cl

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