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Mathematica 9 (2012)

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Virtual Book > Mathematics and Algorithms > Constrained Optimization
MATHEMATICA OVERVIEW

Constrained Optimization

IntroductionIntroduction

Optimization Problems

Global Optimization

Local Optimization

Solving Optimization Problems

Linear OptimizationLinear Optimization

Introduction

The LinearProgramming Function

ExamplesExamples

Difference between Interior Point and Simplex and/or Revised Simplex

Finding Dual Variables

Dealing with Infeasibility and Unboundedness in the Interior Point Method

The Method Options of "InteriorPoint"

Importing Large Datasets and Solving Large-Scale ProblemsImporting Large Datasets and Solving Large-Scale Problems

Importing MPS Formatted Files in Equation Form

Large-Scale Problems: Importing in Matrix and Vector Form

Free Formatted MPS Files

Application Examples of Linear ProgrammingApplication Examples of Linear Programming

L1 Norm Minimization

Design of an Optimal Anchor

Algorithms for Linear ProgrammingAlgorithms for Linear Programming

Simplex and Revised Simplex Algorithms

Interior Point Algorithm

Numerical Nonlinear Local OptimizationNumerical Nonlinear Local Optimization

Introduction

The FindMinimum FunctionThe FindMinimum Function

Options for FindMinimum

Examples of FindMinimumExamples of FindMinimum

Finding a Global Minimum

Solving Minimax Problems

Multiobjective Optimization: Goal Programming

An Application Example

Limitations of Interior Point Method

Numerical Algorithms for Constrained Local OptimizationNumerical Algorithms for Constrained Local Optimization

The Interior Point Algorithm

Numerical Nonlinear Global OptimizationNumerical Nonlinear Global Optimization

Introduction

The NMinimize Function

Numerical Algorithms for Constrained Global OptimizationNumerical Algorithms for Constrained Global Optimization

Nelder-Mead

Differential Evolution

Simulated Annealing

Random Search

Numerical Nonlinear Global Optimization Examples

Exact Global OptimizationExact Global Optimization

Introduction

Algorithms

Optimization by Cylindrical Algebraic DecompositionOptimization by Cylindrical Algebraic Decomposition

Examples

Customized CAD Algorithm for Optimization

Reduction to Minimizing a Coordinate Function

The Projection Phase of CAD

The Lifting Phase of CAD

Strict Inequality Constraints

Linear Optimization

Univariate Optimization

Optimization by Finding Stationary and Singular Points

Optimization over the IntegersOptimization over the Integers

Integer Linear Programming

Optimization over the Reals Combined with Integer Solution Finding

Comparison of Constrained Optimization Functions

Constrained Optimization References

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