An Introduction to Optimization, 4th Edition

An Introduction to Optimization (Wiley Series in Discrete Mathematics and Optimization)
Praise for the Third Edition “. . . guides and leads the reader through the learning path . . . [e]xamples are stated very clearly and the results are presented with attention to detail.”  —MAA Reviews

Fully updated to reflect new developments in the field, the Fourth Edition of Introduction to Optimization fills the need for accessible treatment of optimization theory and methods with an emphasis on engineering design. Basic definitions and notations are provided in addition to the related fundamental background for linear algebra, geometry, and calculus.

This new edition explores the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. The authors also present an optimization perspective on global search methods and include discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm.  Featuring an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, the Fourth Edition also offers:

A new chapter on integer programming

Expanded coverage of one-dimensional methods

Updated and expanded sections on linear matrix inequalities

Numerous new exercises at the end of each chapter

MATLAB exercises and drill problems to reinforce the discussed theory and algorithms

Numerous diagrams and figures that complement the written presentation of key concepts

MATLAB M-files for implementation of the discussed theory and algorithms (available via the book’s website)

Introduction to Optimization, Fourth Edition is an ideal textbook for courses on optimization theory and methods. In addition, the book is a useful reference for professionals in mathematics, operations research, electrical engineering, economics, statistics, and business.

Table of Contents

PART I MATHEMATICAL REVIEW
1 Methods of Proof and Some Notation 3
2 Vector Spaces and Matrices 7
3 Transformations 25
4 Concepts from Geometry 45
5 Elements of Calculus 55

PART II UNCONSTRAINED OPTIMIZATION
6 Basics of Set-Constrained and Unconstrained Optimization 81
7 One-Dimensional Search Methods 103
8 Gradient Methods 131
9 Newton’s Method 161
10 Conjugate Direction Methods 175
11 Quasi-Newton Methods 193
12 Solving Linear Equations 217
13 Unconstrained Optimization and Neural Networks 253
14 Global Search Algorithms 273

PART III LINEAR PROGRAMMING
15 Introduction to Linear Programming 305
16 Simplex Method 339
17 Duality 379
18 Nonsimplex Methods 403
19 Integer Linear Programming 429

PART IV NONLINEAR CONSTRAINED OPTIMIZATION
20 Problems with Equality Constraints 453
21 Problems with Inequality Constraints 487
22 Convex Optimization Problems 509
23 Algorithms for Constrained Optimization 549
24 Multiobjective Optimization 577