1st Edition
Introduction to Linear Optimization and Extensions with MATLAB®
Linear Programming
Introduction
General Linear Programming Problems
More Linear Programming Examples
Exercises
Computational Project
Geometry of Linear Programming
Introduction
Geometry of the Feasible Set
Extreme Points and Basic Feasible Solutions
Resolution (Representation) Theorem
Exercises
The Simplex Method
Introduction
Simplex Method Development
Generating an Initial Basic Feasible Solution (Two-Phase and Big M Methods)
Degeneracy and Cycling
Revised Simplex Method
Complexity of the Simplex Method
Simplex Method MATLAB Code
Exercises
Duality Theory
Introduction
Motivation for Duality
Forming the Dual Problem for General Linear Programs
Weak and Strong Duality Theory
Complementary Slackness
Duality and the Simplex Method
Economic Interpretation of the Dual
Sensitivity Analysis
Exercises
Dantzig-Wolfe Decomposition
Introduction
Decomposition for Block Angular Linear Programs
Master Problem Reformulation
Restricted Master Problem and the Revised Simplex Method
Dantzig-Wolfe Decomposition
Dantzig-Wolfe MATLAB Code
Exercises
Interior Point Methods
Introduction
Linear Programming Optimality Conditions
Primal-Dual Interior Point Strategy
The Predictor-Corrector Variant of the Primal-Dual Interior Point Method
Primal-Dual Interior Point Method in MATLAB
Exercises
Quadratic Programming
Introduction
QP Model Structure
QP Application: Financial Optimization
Solving Quadratic Programs Using MATLAB
Optimality Conditions for Quadratic Programming
Exercises
Linear Optimization under Uncertainty
Introduction
Stochastic Programming
More Stochastic Programming Examples
Robust Optimization
Exercises
A Linear Algebra Review
Bibliography
Biography
Roy H Kwon is a professor at University of Toronto - St. George Campus, Canada.
"The book goes beyond a `cookbook' for linear optimization in Matlab; instead it outlines and explains the theory behind each linear optimization technique and a number of essential theorems are provided and proven. This greatly helps the reader understand why each technique works and how it is implemented in the Matlab software. Computational projects suggested in the book can also assist students with the practical implementation of the techniques in real-life applications.
—Efstratios Rappos (Aubonne) in Zentralblatt, MATH 1287
