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Matrices and Simplex Algorithms

A Textbook in Mathematical Programming and Its Associated Mathematical Topics

  • A. R. G. Heesterman

Table of contents

  1. Front Matter
    Pages i-x
  2. Matrices, Block-Equations, and Determinants

    1. Front Matter
      Pages 1-2
    2. A. R. G. Heesterman
      Pages 3-4
    3. A. R. G. Heesterman
      Pages 5-32
    4. A. R. G. Heesterman
      Pages 33-61
    5. A. R. G. Heesterman
      Pages 62-67
    6. A. R. G. Heesterman
      Pages 68-111
  3. Graphs and Linear Programming

    1. Front Matter
      Pages 112-114
    2. A. R. G. Heesterman
      Pages 115-143
    3. A. R. G. Heesterman
      Pages 144-148
    4. A. R. G. Heesterman
      Pages 149-180
    5. A. R. G. Heesterman
      Pages 181-204
    6. A. R. G. Heesterman
      Pages 205-222
    7. A. R. G. Heesterman
      Pages 223-241
    8. A. R. G. Heesterman
      Pages 242-272
    9. A. R. G. Heesterman
      Pages 273-317
  4. Some General Mathematical Programming Notions and Related Matrix Algebra

    1. Front Matter
      Pages 318-318
    2. A. R. G. Heesterman
      Pages 363-399
  5. Quadratic Programming

    1. Front Matter
      Pages 400-401
    2. A. R. G. Heesterman
      Pages 402-515
    3. A. R. G. Heesterman
      Pages 516-555
    4. A. R. G. Heesterman
      Pages 556-635
  6. Integer Programming

    1. Front Matter
      Pages 636-636
    2. A. R. G. Heesterman
      Pages 637-655
    3. A. R. G. Heesterman
      Pages 656-701
    4. A. R. G. Heesterman
      Pages 702-772
  7. Back Matter
    Pages 773-790

About this book

Introduction

This is a textbook devoted to mathematical programming algorithms and the mathematics needed to understand such algorithms. It was mainly written for economists, but the mathematics itself obviously has relevance for other disciplines. It is a textbook as well a~ in parts, a contribution to new knowledge. There is, accordingly, a broad ordering of climbing sophistication, the earlier chapters being purely for the student, the later chapters being more specialist and containing some element of novelty on certain points. The book is edited in five parts. Part I deals with elementary matrix operations, matrix inversion, determinants, etc. Part II is mainly devoted to linear programming. As far as students' readability is concerned, these two parts are elementary undergraduate material. However, I would claim, in particular with respect to linear programming, that I do things more efficiently than the standard textbook approach has it. This refers mainly to the search for a feasible solution i.e. Chapter 9, and to upper and lower limits, i.e. Chapter 10. I have also argued that the standard textbook treatment of degeneracy misses a relevant problem, namely that of accuracy. In short, I would invite anyone who has the task of writing or designing an LP-code, to first acquaint himself with my ideas. viii INTRODUCTION Parts III and IV are concerned with nonlinear programming.

Keywords

Mathematica algebra algorithms linear optimization programming

Authors and affiliations

  • A. R. G. Heesterman
    • 1
  1. 1.Department of EconomicsUniversity of BirminghamUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-7941-3
  • Copyright Information Springer Science+Business Media B.V. 1983
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-009-7943-7
  • Online ISBN 978-94-009-7941-3
  • Buy this book on publisher's site