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Linear Programming: Mathematics, Theory and Algorithms

  • Book
  • © 1996

Overview

Editors:
  1. Michael J. Panik

    1. University of Hartford, USA

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Part of the book series: Applied Optimization (APOP, volume 2)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction and Overview

    • Michael J. Panik
    Pages 1-8

  3. Preliminary Mathematics

    • Michael J. Panik
    Pages 9-68

  4. Introduction to Linear Programming

    • Michael J. Panik
    Pages 69-88

  5. Duality Theory

    • Michael J. Panik
    Pages 89-110

  6. The Theory of Linear Programming

    • Michael J. Panik
    Pages 111-139

  7. Duality Theory Revisited

    • Michael J. Panik
    Pages 141-168

  8. Computational Aspects of Linear Programming

    • Michael J. Panik
    Pages 169-193

  9. One-Phase, Two-Phase, and Composite Methods of Linear Programming

    • Michael J. Panik
    Pages 195-231

  10. Computational Aspects of Linear Programming: Selected Transformations

    • Michael J. Panik
    Pages 233-250

  11. The Dual Simplex, Primal-Dual, and Complementary Pivot Methods

    • Michael J. Panik
    Pages 251-288

  12. Postoptimality Analysis I

    • Michael J. Panik
    Pages 289-318

  13. Postoptimality Analysis II

    • Michael J. Panik
    Pages 319-340

  14. Interior Point Methods

    • Michael J. Panik
    Pages 341-431

  15. Interior Point Algorithms for Solving Linear Complementarity Problems

    • Michael J. Panik
    Pages 433-458

  16. Back Matter

    Pages 459-497
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Keywords

About this book

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.

Reviews

` ... a carefully written textbook in a clear style. It is a very informative introduction to this field and may be recommended to students as well as to everybody interested in this special field of applied mathematics.'
Optimization, 43 (1998)

Editors and Affiliations

  • University of Hartford, USA

    Michael J. Panik

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