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Linear Programming Computation

  • Book
  • © 2014

Overview

Authors:
  1. Ping-Qi PAN

    1. Department of Mathematics, Southeast University, Nanjing, China

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  • A landmark work on LP

  • Includes a wealth of rich and advanced materials

  • A must-read for all students, researchers and practitioners interested in LP and related areas

  • Includes supplementary material: sn.pub/extras

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Introduction

    • Ping-Qi PAN
    Pages 1-24

  3. Fundamentals

    1. Front Matter

      Pages 25-25
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    2. Geometry of the Feasible Region

      • Ping-Qi PAN
      Pages 27-60

    3. Simplex Method

      • Ping-Qi PAN
      Pages 61-100

    4. Duality Principle and Dual Simplex Method

      • Ping-Qi PAN
      Pages 101-121

    5. Implementation of the Simplex Method

      • Ping-Qi PAN
      Pages 123-141

    6. Sensitivity Analysis and Parametric LP

      • Ping-Qi PAN
      Pages 143-167

    7. Variants of the Simplex Method

      • Ping-Qi PAN
      Pages 169-203

    8. Decomposition Method

      • Ping-Qi PAN
      Pages 205-238

    9. Interior-Point Method

      • Ping-Qi PAN
      Pages 239-273

    10. Integer Linear Programming (ILP)

      • Ping-Qi PAN
      Pages 275-294

  4. Advanced Topics

    1. Front Matter

      Pages 295-295
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    2. Pivot Rule

      • Ping-Qi PAN
      Pages 297-309

    3. Dual Pivot Rule

      • Ping-Qi PAN
      Pages 311-319

    4. Simplex Phase-I Method

      • Ping-Qi PAN
      Pages 321-339

    5. Dual Simplex Phase-l Method

      • Ping-Qi PAN
      Pages 341-356

    6. Reduced Simplex Method

      • Ping-Qi PAN
      Pages 357-385

    7. Improved Reduced Simplex Method

      • Ping-Qi PAN
      Pages 387-407

    8. D-Reduced Simplex Method

      • Ping-Qi PAN
      Pages 409-440
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Keywords

About this book

With emphasis on computation, this book is a real breakthrough in the field of LP. In addition to conventional topics, such as the simplex method, duality, and interior-point methods, all deduced in a fresh and clear manner, it introduces the state of the art by highlighting brand-new and advanced results, including efficient pivot rules, Phase-I approaches, reduced simplex methods, deficient-basis methods, face methods, and pivotal interior-point methods. In particular, it covers the determination of the optimal solution set, feasible-point simplex method, decomposition principle for solving large-scale problems, controlled-branch method based on generalized reduced simplex framework for solving integer LP problems.

Reviews

“Evidenced by superior performance in computational experiments, the author’s work has refreshed the state of the art of LP, and by its originality, breadth and depth, is having a major impact on the field of mathematical optimization.” (EJOR, European Journal of Operational Research, Vol. 267 (3), June, 2018)

“The book seems to be mainly addressed to scientists who already possess some expertise in LP. The kind of presentation, however, also allows using parts of it as a basis for a course on the topic. In fact, a special feature of the book is that an algorithm typically is accompanied by some example for which the results of all computational steps needed to find a solution are written down.” (Rembert Reemtsen, zbMATH, Vol. 1302, 2015)

“This book is a research monograph focusing on computational techniques in the simplex method for linear programming. … It may be of interest to researchers and developers of simplex method codes for linear programming.” (B. Borchers, Choice, Vol. 52 (3), November, 2014)

Authors and Affiliations

  • Department of Mathematics, Southeast University, Nanjing, China

    Ping-Qi PAN

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