Nonlinear Optimization with Engineering Applications

By: Michael Bartholomew-Biggs

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Hardcover | 22 August 2008

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300 Pages

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24.13 x 15.88 x 2.54

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This book, like its companion volume Nonlinear Optimization with Financial Applications, is an outgrowth of undergraduate and po- graduate courses given at the University of Hertfordshire and the University of Bergamo. It deals with the theory behind numerical methods for nonlinear optimization and their application to a range of problems in science and engineering. The book is intended for ?nal year undergraduate students in mathematics (or other subjects with a high mathematical or computational content) and exercises are provided at the end of most sections. The material should also be useful for postg- duate students and other researchers and practitioners who may be c- cerned with the development or use of optimization algorithms. It is assumed that readers have an understanding of the algebra of matrices and vectors and of the Taylor and mean value theorems in several va- ables. Prior experience of using computational techniques for solving systems of linear equations is also desirable, as is familiarity with the behaviour of iterative algorithms such as Newton's methodfor nonlinear equations in one variable. Most of the currently popular methods for continuous nonlinear optimization are described and given (at least) an intuitive justi?cation. Relevant convergence results are also outlined and we provide proofs of these when it seems instructive to do so. This theoretical material is complemented by numerical illustrations which give a ?avour of how the methods perform in practice.

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"This book gives on 280 pages a broad overview of nonlinear optimization. ... The presented optimization approaches are compared with each other by means of several examples with up to 200 variables. ... the introduction of the different techniques is written in a very comprehensible way. ... each section contains exercises to verify and deepen the understanding of the material." (Andrea Walther, Zentralblatt MATH, Vol. 1167, 2009)

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Engineering & Technology Technology in General Engineering in General Optimisation Linear Programming Business & Management Operational Research Applied Mathematics Probability & Statistics

List of Figures
List of Tables
Introducing Optimization	p. 1
One-variable Optimization	p. 11
Applications in n Variables	p. 33
n-Variable Unconstrained Optimization	p. 41
Direct Search Methods	p. 53
Computing Derivatives	p. 63
The Steepest Descent Method	p. 75
Weak Line Searches and Convergence	p. 83
Newton and Newton-like Methods	p. 91
Quasi-Newton Methods	p. 107
Conjugate Gradient Methods	p. 119
A Summary of Unconstrained Methods	p. 131
Larger-Scale Problems	p. 141
Global Unconstrained Optimization	p. 147
Equality Constrained Optimization	p. 155
Linear Equality Constraints	p. 169
Penalty Function Methods	p. 183
Sequential Quadratic Programming	p. 197
Inequality Constrained Optimization	p. 211
Extending Equality Constraint Methods	p. 225
Barrier Function Methods	p. 239
Interior Point Methods	p. 249
A Summary of Constrained Methods	p. 259
The OPTIMA Software	p. 261
References	p. 273
Index	p. 277
Table of Contents provided by Blackwell. All Rights Reserved.

Nonlinear Optimization with Engineering Applications

At a Glance

Hardcover

Industry Reviews

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