Linear Programming: Mathematics, Theory and Algorithms

✍ Scribed by Michael J. Panik (auth.), Michael J. Panik (eds.)

• Publisher: Springer US
• Year: 1996
• Tongue: English
• Leaves: 502
• Series: Applied Optimization 2
• Edition: 1
• Category: Library

✦ Synopsis

Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory.
Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

✦ Table of Contents

Front Matter....Pages i-xi
Introduction and Overview....Pages 1-8
Preliminary Mathematics....Pages 9-68
Introduction to Linear Programming....Pages 69-88
Duality Theory....Pages 89-110
The Theory of Linear Programming....Pages 111-139
Duality Theory Revisited....Pages 141-168
Computational Aspects of Linear Programming....Pages 169-193
One-Phase, Two-Phase, and Composite Methods of Linear Programming....Pages 195-231
Computational Aspects of Linear Programming: Selected Transformations....Pages 233-250
The Dual Simplex, Primal-Dual, and Complementary Pivot Methods....Pages 251-288
Postoptimality Analysis I....Pages 289-318
Postoptimality Analysis II....Pages 319-340
Interior Point Methods....Pages 341-431
Interior Point Algorithms for Solving Linear Complementarity Problems....Pages 433-458
Back Matter....Pages 459-497

✦ Subjects

Optimization; Operations Research/Decision Theory; Economic Theory; Game Theory, Economics, Social and Behav. Sciences