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An Introduction to Optimization, 2nd Edition

An Introduction to Optimization, 2nd Edition

Edwin K. P. Chong, Stanislaw H. Zak

ISBN: 978-0-471-65400-1

Apr 2004

496 pages

Select type: E-Book



A modern, up-to-date introduction to optimization theory and methods
This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Second Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization.
Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked examples to illustrate both theory and algorithms, this book also provides:
* A review of the required mathematical background material
* A mathematical discussion at a level accessible to MBA and business students
* A treatment of both linear and nonlinear programming
* An introduction to recent developments, including neural networks, genetic algorithms, and interior-point methods
* A chapter on the use of descent algorithms for the training of feedforward neural networks
* Exercise problems after every chapter, many new to this edition
* MATLAB(r) exercises and examples
* Accompanying Instructor's Solutions Manual available on request
An Introduction to Optimization, Second Edition helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business.

An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
Preface. xiii


Methods of Proof and Some Notation 1

Vector Spaces and Matrices 5

Transformations 21

Concepts from Geometry 39

Elements of Calculus 49


Basics of Set-Constrained and Unconstrained Optimization 73

One-Dimensional Search Methods 91

Gradient Methods 113

Newton's Method 139

Conjugate Direction Methods 151

Quasi-Newton Methods 167

Solving Ax = b 187

Unconstrained Optimization and Neural Networks 219

Genetic Algorithms 237


Introduction to Linear Programming. 255

Simplex Method 287

Duality 321

Non-Simplex Methods 339


Problems with Equality Constraints 365

Problems with Inequality Constraints 397

Convex Optimization Problems 417

Algorithms for Constrained Optimization 439

References 455

Index 462
" excellent introduction to optimization theory..." (Journal of Mathematical Psychology, 2002)

"A textbook for a one-semester course on optimization theory and methods at the senior undergraduate or beginning graduate level." (SciTech Book News, Vol. 26, No. 2, June 2002)