Linear Optimization

This undergraduate textbook is written for a junior/senior level course on linear optimization. Unlike other texts, the treatment allows the use of the "modified Moore method" approach by working examples and proof opportunities into the text in order to encourage students to develop some of the content through their own experiments and arguments while reading the text. Additionally, the focus is on the mathematics underlying the ideas of optimizing linear functions under linear constraints and the algorithms used to solve them. In particular, the author uses the Simplex Algorithm to motivate these concepts. The text progresses at a gentle and inviting pace. The presentation is driven by numerous examples and illustrations. Ample exercises are provided at the end of each chapter for mastering the material. Opportunities for integrating Maple (or similar) software are included in the book. The author's own WebSim software can be freely downloaded from his website for pedagogical use. The teacher's version of the text contains solutions embedded within the text, rather than in an appendix. It also has extra material and suggestions for the teacher's benefit. Junior/senior level undergraduate students will benefit from the book, as will beginning graduate students. Future secondary school mathematics teachers will also find this book useful. Book jacket.

Arizona State University Professor Glenn H. Hurlbert has published nearly 50 articles in graph theory, combinatorics, and optimization, and has been the recipient of numerous teaching and mentoring awards from ASU, the ASU Parents Association, the School of Mathematical and Statistical Sciences, and the Mathematical Association of America.

Preface	p. vii
Introduction	p. 1
The Diet Problem	p. 1
The Matching Problem	p. 4
Un Problema de la Práctica	p. 7
Standard Form and the Dual	p. 8
Exercises	p. 12
The Simplex Algorithm	p. 29
Geometric Lens	p. 29
Algebraic Lens	p. 32
$$$	p. 37
Infeasible Basis	p. 38
Shortcut Method	p. 41
Infeasibility	p. 45
Unboundedness	p. 47
Cycling	p. 48
The Fundamental Theorem	p. 49
Exercises	p. 50
Geometry	p. 59
Extreme Points	p. 59
Convexity	p. 61
$$$	p. 64
Carathéodory's Theorem	p. 65
Exercises	p. 67
The Duality Theorem	p. 73
Primal-Dual Relationship	p. 73
Complementary Slackness Conditions	p. 77
Jizoezi, Jizoezi, Jizoezi	p. 79
Finding Optimal Certificates	p. 80
Exercises	p. 82
Matrix Environment	p. 89
Format and Dictionaries	p. 89
Simplex Phases and Advantages	p. 91
$$$	p. 97
Basic Coefficients	p. 98
Exercises	p. 100
General Form	p. 107
Nonstandard Duals	p. 107
General Simplex and Phase 0	p. 110
Plus de Pratique	p. 113
General Duality and Slackness	p. 113
Exercises	p. 115
Unsolvable Systems	p. 119
Infeasible Certificates	p. 119
Inconsistency	p. 122
$$$	p. 124
Unsolvable Subsystems	p. 124
Exercises	p. 126
Geometry Revisited	p. 129
Helly's Theorem	p. 129
Permutation Matrices	p. 131
Pratique de Novo	p. 134
Cones	p. 134
Exercises	p. 137
Game Theory	p. 145
Matrix Games	p. 145
Minimax Theorem	p. 147
Bitte Praxis	p. 150
Saddles	p. 151
Exercises	p. 155
Network Environment	p. 163
Shipping	p. 163
Trees	p. 167
Nilai!	p. 172
Integrality	p. 173
Exercises	p. 174
Combinatorics	p. 183
Hatchings	p. 183
Covers	p. 185
$$$	p. 188
Systems of Distinct Representatives	p. 189
Exercises	p. 190
Economics	p. 195
Shadow Prices	p. 195
Reduced Costs	p. 200
Gyakoroljon egy Kicsit	p. 202
Dual Simplex	p. 203
Exercises	p. 206
Integer Optimization	p. 209
Cutting Planes	p. 209
Branch-and-Bound	p. 215
$$$	p. 221
Integer Certificates	p. 222
Exercises	p. 223
Linear Algebra Review	p. 231
Equivalence of Auxiliary and Shortcut Methods	p. 235
Complexity	p. 241
P versus IMP	p. 241
Examples	p. 243
LO Complexity	p. 244
Software	p. 247
WebSim	p. 247
Algorithms	p. 248
Maple	p. 250
Index	p. 257
Table of Contents provided by Ingram. All Rights Reserved.

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