This book on constrained optimization is novel in that it fuses these themes: • use examples to introduce general ideas; • engage the student in spreadsheet computation; • survey the uses of constrained optimization;. • investigate game theory and nonlinear optimization, • link the subject to economic reasoning, and • present the requisite mathematics. Blending these themes makes constrained optimization more accessible and more valuable. It stimulates the student’s interest, quickens the learning process, reveals connections to several academic and professional fields, and deepens the student’s grasp of the relevant mathematics. The book is designed for use in courses that focus on the applications of constrained optimization, in courses that emphasize the theory, and in courses that link the subject to economics.
Author(s): Eric V. Denardo (auth.)
Series: International Series in Operations Research & Management Science 149
Edition: 1
Publisher: Springer US
Year: 2011
Language: English
Pages: 673
Tags: Operation Research/Decision Theory; Operations Research, Management Science; Mathematical Modeling and Industrial Mathematics; Optimization; Engineering Economics, Organization, Logistics, Marketing; Industrial and Production Engineering
Front Matter....Pages 1-1
Front Matter....Pages 1-1
Introduction to Linear Programs....Pages 3-32
Spreadsheet Computation....Pages 33-66
Mathematical Preliminaries....Pages 67-109
Front Matter....Pages 111-111
The Simplex Method, Part 1....Pages 113-152
Analyzing Linear Programs....Pages 153-194
The Simplex Method, Part 2....Pages 195-218
Front Matter....Pages 219-219
A Survey of Optimization Problems....Pages 221-268
Path Length Problems and Dynamic Programming....Pages 269-295
Flows in Networks....Pages 297-327
Front Matter....Pages 329-330
Vector Spaces and Linear Programs....Pages 331-353
Multipliers and the Simplex Method....Pages 355-375
Duality....Pages 377-412
The Dual Simplex Pivot and Its Uses....Pages 413-441
Front Matter....Pages 443-443
Introduction to Game Theory....Pages 445-478
A Bi-Matrix Game....Pages 479-505
Fixed Points and Equilibria....Pages 507-541
Front Matter....Pages 543-544
Convex Sets....Pages 545-564
Differentiation....Pages 565-579
Convex Functions....Pages 581-615
Nonlinear Programs....Pages 617-661
Back Matter....Pages 567-567
