Linear Programming Using MATLAB

This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book  are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms.

As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus.  The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting rules, basis update methods, and sensitivity analysis.

Table of Contents

Chapter 1 Introduction
Chapter 2 Linear Programming Algorithms
Chapter 3 Linear Programming Benchmark And Random Problems
Chapter 4 Presolve Methods
Chapter 5 Scaling Techniques
Chapter 6 Pivoting Rules
Chapter 7 Basis Inverse And Update Methods
Chapter 8 Revised Primal Simplex Algorithm
Chapter 9 Revised Dual Simplex Algorithm
Chapter 10 Exterior Point Simplex Algorithm
Chapter 11 Interior Point Methods
Chapter 12 Sensitivity Analysis
Appendix A Matlab’S Optimization Toolbox Algorithms
Appendix B State-Of-The-Art Linear Programming Solvers: Clp And Cplex