l13 optimization using excel

Download L13 Optimization using Excel

Post on 14-Jan-2016

30 views

Category:

Documents

1 download

Embed Size (px)

DESCRIPTION

L13 Optimization using Excel. See revised schedule read 8(1-4) + Excel “help” for Mar 12 Test Answers Review: Convex Prog. Prob. Worksheet modifications Excel optimization Summary. Trendline in Excel. Excel help “trendline” for Wed. Theorem 4.9. Given:. S is convex if: - PowerPoint PPT Presentation

TRANSCRIPT

  • L13 Optimization using ExcelSee revised scheduleread 8(1-4) + Excel help for Mar 12Test AnswersReview: Convex Prog. Prob.Worksheet modificationsExcel optimizationSummary*

  • Trendline in Excel*Excel help

    trendline

    for Wed

  • Theorem 4.9*Given:S is convex if:1. hi are linear2. gj are convex i.e. Hg PD or PSDWhen f(x) and S are convex= convex programming problem

  • Sufficient Theorem 4.10, pg 165*The first-order KKT conditions are Necessary and Sufficient for a GLOBAL minimum.if:

    1. f(x) is convexHf(x) Positive definite2. x is defined as a convex feasible set SEquality constraints must be linearInequality constraints must be convex

    HINT: linear functions are convex!

  • Worksheet Modifications Naming cellsInserting shapesInserting MS Equation objectRecording macrosAttaching a macro to a shapeCreating a SOLVER hot buttonVisual basic, tools/references/solver*

  • *Figure 6.1 Excel worksheet for finding roots of 2x/3 sin x : (a) worksheet; (b) worksheet with formulas showing.Excel Applications

  • Solver parameters*Figure 6.2 A Solver Parameters dialog box to define the problem.

  • *Figure 6.3 A Solver Results dialog box and the final worksheet.

  • *Figure 6.4 A Solver Answer Report for roots of 2x/3 sin x = 0.

  • *Figure 6.5 Worksheet and Solver Parameters dialog box for KKT conditions for Example 4.31.

  • *Figure 6.6 Solver Results for KKT conditions for Example 4.31.

  • KKT system of NL EQNsProb 4.59 and 4.122 *

  • *Figure 6.7 Excel worksheet and Solver Parameters dialog box for unconstrained problem.

  • Constrained OptimizationProb. 4.69 and 4.122*

  • Graphical Solution*21

  • *Figure 6.8 Excel worksheet for the linear programming problem.

  • *Figure 6.9 Solver Parameters dialog box for the linear programming problem.

  • *Figure 6.10 Solver Results dialog box for the linear programming problem.

  • *Figure 6.11 Answer Report from Solver for linear programming problem.

  • *Figure 6.12 Sensitivity Report from Solver for the linear programming problem.

  • *Figure 6.13 Excel worksheet for the spring design problem.

  • SummaryKKT pt from a Convex Prog. Prob. Is a global min!Use modifications for ease of usePay attention to layoutDesign variablesParametersAnalysis/Performance VariablesObjective functionConstraintsMay need multiple starting points

    *

    *************