Introduction to linear optimization and extensions with MATLAB (Q2904679)

This book, split into eight chapters, provides a detailed study of linear optimization theory and techniques using Matlab. The book begins with an introduction to linear programming, the standard form of a problem and the types of possible constraints and includes several examples of real-life problems. The second chapter considers the geometrical interpretation of a linear problem and its solution which helps explain some terms such as degeneracy and the fundamental theorem of linear programming. The third chapter moves to discuss the Simplex algorithm for solving linear programs, including the two-phase method, Bland's rule and termination and complexity issues. The author then studies the theory of duality; this is well-explained with several examples and the chapter ends with a description of the dual simplex method and sensitivity analysis issues.NEWLINENEWLINEThe fifth and sixth chapters study more complex linear programming notions such as the Dantzig-Wolfe decomposition and interior point methods for the solution of linear programs. The seventh chapter provides an introduction to quadratic programming and convex optimization. These quadratic problems are inherently linked to linear programming and therefore their study here is well-placed. The last chapter considers problems under uncertainty including several versions of stochastic programming problems.NEWLINENEWLINEEach chapter contains a large number of examples and exercises, as well as detailed Matlab code relevant to each idea studied. Supplementary material for each chapter is provided by the author at the publisher's website. 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.