# An Introduction to Optimization

## Edwin K. P. Chong and Stanislaw H. Żak

Wiley-Interscience Series in Discrete Mathematics and Optimization
John Wiley & Sons, Inc.
New York
ISBN 0-471-08949-4, xiii+409 pp.

NOTICE: Please see the Second Edition.
From the back cover:

## An up-to-date, accessible introduction to an increasingly important field

This timely authoritative book fills a growing need for an introductory text to optimization methods and theory at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization 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-out examples to illustrate both theory and algorithms, this book 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 the most recent developments, including neural networks, genetic algorithms, and the nonsimplex method of Karmarkar
• A chapter on the use of descent algorithms for the training of neural networks
• Exercise problems after every chapter
• MATLAB exercises and examples
• An optional solutions manual with MATLAB source listings
(Instructors only: To obtain a copy of the solutions manual, see ordering information below.)
This book helps students to 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.

## Errata

An up-to-date errata is available, in Postscript and PDF formats.

Preface

### Part I. Mathematical Review

1 Methods of Proof and Some Notation
2 Real Vector Spaces and Matrices
3 Transformations
4 Concepts from Geometry
5 Elements of Differential Calculus

### Part II. Unconstrained Optimization

6 Basics of Unconstrained Optimization
7 One-Dimensional Search Methods
9 Newton's Method
10 Conjugate Direction Methods
11 Quasi-Newton Methods
12 Solving Ax=b
13 Unconstrained Optimization and Feedforward Neural Networks
14 Genetic Algorithms

### Part III. Linear Programming

15 Introduction to Linear Programming
16 The Simplex Method
17 Duality
18 Non-Simplex Methods

### Part IV. Nonlinear Constrained Optimization

19 Problems with Equality Constraints
20 Problems With Inequality Constraints
21 Convex Optimization Problems
22 Algorithms for Constrained Optimization
Bibliography
Index

## Ordering information

Wiley has information on how to order the book.

Instructors only: Copies of the solutions manuals are held in-house at Wiley's New York office. For a copy of the solutions manual, fax an official request letter on university letterhead to 201-748-6825, or contact Sari Friedman (sfriedman@wiley.com)

Professor Edwin Chong,