Numerical Methods of Mathematical Optimization (eBook)

Front Cover 1
Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs 4
Copyright Page 5
Table of Contents 8
PREFACE TO THE GERMAN EDITION 6
Chapter 1. Linear Optimization 10
1.1 General Formulation of Linear Optimization 10
1.2 The Simplex Method 15
1.3 Determination of a Feasible Initial Solution 22
1.4 The Fundamental Theorem and the Simplex Criterion of the Linear Optimization Theory 28
1.5 Degeneracies 36
1.6 Dual Linear Optimization Problems 39
1.7 The Dual Simplex Method 43
1.8 The Revised Simplex Method 46
1.9 The Decomposition Algorithm 50
1.10 The Duoplex Algorithm 58
1.11 Linear Integer Optimization 64
Chapter 2. Nonlinear Optimization 69
2.1 Convex Domains and Functions 69
2.2 General Nonlinear Optimization 71
2.3 Convex Optimization 72
2.4 The Kuhn–Tucker Conditions 73
2.5 Quadratic Optimization 75
2.6 Duality in the Case of Quadratic Optimization 77
2.7 The Method of Beale 77
2.8 The Methtod of Wolfe 83
2.9 A Look at Further Methods 90
Chapter 3. Explanations of the Computer Programs 93
3.1 The Subroutine System 93
3.2 The Use of the Optimization Programs 94
3.3 Numerical Properties 95
3.4 General Discussion of Variable Notations and Storage Organization 96
3.5 Properties of Individual Optimization Programs 98
Chapter 4. ALGOL and FORTRAN Programs 109
4.1 Global Procedures 109
4.2 ALGOL Program for the Simplex Method 122
4.3 FORTRAN Program for the Simplex Method 124
4.4 ALGOL Program for the Dual Simplex Method 127
4.5 FORTRAN Program for the Dual Simplex Method 128
4.6 ALGOL Program for the Revised Simplex Method 130
4.7 FORTRAN Program for the Revised Simplex Method 133
4.8 ALGOL Program for the Decomposition Algorithm 136
4.9 FORTRAN Program for the Decomposition Algorithm 137
4.10 ALGOL Program for the Duoplex Method 139
4.11 FORTRAN Program for the Duoplex Method 142
4.12 ALGOL Program for the Gomory Algorithm 147
4.13 FORTRAN Program for the Gomory Algorithm 148
4.14 ALGOL Program for the Beale Algorithm 149
4.15 FORTRAN Program for the Beale Algorithm 151
4.16 ALGOL Program for the Wolfe Algorithm 154
4.17 FORTRAN Program for the Wolfe Algorithm 158
LIST OF EXISTING COMPUTER PROGRAMS 163
BIBLIOGRAPHY 171
ADDENDUM: Version of the Computer Programs for Practical Application 178
INDEX 226