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Linear programming with MATLAB. (English) Zbl 1147.90027

MPS/SIAM Series on Optimization 7. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-43-6/pbk). xi, 266 p. (2007).
The book aims to provide elementary introduction to linear programming formulation, algorithms, computations, and application. One feature of the authors’ approach is the use of MATLAB codes to demonstrate the computational aspects of the the course, from the elementary manipulations that form the building blocks of algorithms to full implementation of revised simplex and interior-point methods. The book is intended for both undergraduates and beginning graduate students from many other departments, including Industrial and Systems Engineering, Statistics, and Mathematics.
Chapter 1 gives an introduction to linear programming. Several other practical problems that can be formulated as linear programs are discussed. Chapter 2 describes the Jordan exchange and its implementation in MATLAB. In the latter part of the chapter, the authors discuss the LU factorization. Chapter 3 describes the simplex method. Chapter 4 deals with the topic of duality. In chapter 5 the authors describe a revised simplex method. They also discuss network flow problems and mention in particular how the simplex approach can be adapted to take advantage of the special structure of these problems. In chapter 6 the authors examine how the solution of a linear programm are affected when changes are made to the data of the problem. Chapter 7 focuses on quadratic programming and complementarity problems. Chapter 8 gives specifics of the interior-point approach. The final chapter deals with approximation and classification problems, showing how these problems can be formulated and solved as linear or quadratic programms.

MSC:

90C05 Linear programming
68W30 Symbolic computation and algebraic computation

Software:

Matlab
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