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Introduction to Linear Optimization and Extensions with MATLAB®

By Roy H. Kwon

CRC Press – 2013 – 362 pages

Series: Operations Research Series

Purchasing Options:

  • Add to CartHardback: $99.95
    978-1-43-986263-6
    September 5th 2013

Description

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.

Contents

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

Author Bio

Roy H Kwon is a professor at University of Toronto - St. George Campus, Canada.

Name: Introduction to Linear Optimization and Extensions with MATLAB® (Hardback)CRC Press 
Description: By Roy H. Kwon. 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...
Categories: Operations Research, Production Systems, Operations Research