Matrices and Simplex Algorithms

1. Front Matter

   Pages i-x

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2. Matrices, Block-Equations, and Determinants

   1. Front Matter

      Pages 1-2

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   2. Equations-Systems and Tableaux

      • A. R. G. Heesterman

      Pages 3-4

   3. Matrix Notation

      • A. R. G. Heesterman

      Pages 5-32

   4. Block-Equations and Matrix-Inversion

      • A. R. G. Heesterman

      Pages 33-61

   5. Some Operators and their Use

      • A. R. G. Heesterman

      Pages 62-67

   6. Determinants and Rank

      • A. R. G. Heesterman

      Pages 68-111

3. Graphs and Linear Programming

   1. Front Matter

      Pages 112-114

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   2. Vectors and Coordinate-Spaces

      • A. R. G. Heesterman

      Pages 115-143

   3. Some Basic Linear Programming Concepts

      • A. R. G. Heesterman

      Pages 144-148

   4. Outline of the Simplex Algorithm

      • A. R. G. Heesterman

      Pages 149-180

   5. The Search for a Feasible Solution

      • A. R. G. Heesterman

      Pages 181-204

   6. Mixed Systems, Upper and Lower Bounds

      • A. R. G. Heesterman

      Pages 205-222

   7. Duality

      • A. R. G. Heesterman

      Pages 223-241

   8. Linear Programming on the Computer

      • A. R. G. Heesterman

      Pages 242-272

   9. Parametric Variatt of the Lp Problem

      • A. R. G. Heesterman

      Pages 273-317

4. Some General Mathematical Programming Notions and Related Matrix Algebra

   1. Front Matter

      Pages 318-318

      PDF

   2. Topology of Feasible Space Areas and its Relation to Definiteness

      • A. R. G. Heesterman

      Pages 319-362

   3. Optimality Conditions

      • A. R. G. Heesterman

      Pages 363-399

5. Quadratic Programming

   1. Front Matter

      Pages 400-401

      PDF

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.

• Mathematica
• algebra
• algorithms
• linear optimization
• programming
• data structures

`The textbook will be very helpful to the reader acquainted with the basic concepts of mathematical programming and interested in numerical details as well as in efficient codes. It will also benefit students as a resource for numerical examples and code details.'
Optima: Mathematical Programming Society Newsletter, 18 (1986)

• Department of Economics, University of Birmingham, UK

  A. R. G. Heesterman

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