1st Edition
Introduction to Linear Optimization and Extensions with MATLAB®
Filling the need for an introductory book on linear programming that discusses the important ways to mitigate parameter uncertainty, Introduction to Linear Optimization and Extensions with MATLAB® provides a concrete and intuitive yet rigorous introduction to modern linear optimization. In addition to fundamental topics, the book discusses current linear optimization technologies such as predictor-path following interior point methods for both linear and quadratic optimization as well as the inclusion of linear optimization of uncertainty i.e. stochastic programming with recourse and robust optimization.
The author introduces both stochastic programming and robust optimization as frameworks to deal with parameter uncertainty. The author’s unusual approach—developing these topics in an introductory book—highlights their importance. Since most applications require decisions to be made in the face of uncertainty, the early introduction of these topics facilitates decision making in real world environments. The author also includes applications and case studies from finance and supply chain management that involve the use of MATLAB.
Even though there are several LP texts in the marketplace, most do not cover data uncertainty using stochastic programming and robust optimization techniques. Most emphasize the use of MS Excel, while this book uses MATLAB which is the primary tool of many engineers, including financial engineers. The book focuses on state-of-the-art methods for dealing with parameter uncertainty in linear programming, rigorously developing theory and methods. But more importantly, the author’s meticulous attention to developing intuition before presenting theory makes the material come alive.
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
