Practical Methods of Optimization [Paperback]

R. Fletcher (Author)

Book Description

ISBN-10: 0471494631 | ISBN-13: 978-0471494638 | Publication Date: May 2000 | Edition: 2

Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers revised coverage of basic theory and standard techniques, with updated discussions of line search methods, Newton and quasi-Newton methods, and conjugate direction methods, as well as a comprehensive treatment of restricted step or trust region methods not commonly found in the literature. Also includes recent developments in hybrid methods for nonlinear least squares; an extended discussion of linear programming, with new methods for stable updating of LU factors; and a completely new section on network programming. Chapters include computer subroutines, worked examples, and study questions.

Editorial Reviews

From the Back Cover

This established textbook is noted for its coverage of optimization methods that are of practical importance. It provides a thorough treatment of standard methods such as linear and quadratic programming, Newton-like methods and the conjugate gradient method. The theoretical aspects of the subject include an extended treatment of optimality conditions and the significance of Lagrange multipliers. The relevance of convexity theory to optimization is also not neglected. A significant proportion of the book is devoted to the solution of nonlinear problems, with an authoritative treatment of current methodology. Thus state of the art techniques such as the BFGS method, trust region methods and the SQP method are described and analysed. Other features are an extensive treatment of nonsmooth optimization and the L_1 penalty function. Contents Part 1 Unconstrained Optimization Part 2 Constrained Optimization
* Introduction
* Structure of Methods
* Newton-like Methods
* Conjugate Direction Methods
* Restricted Step Methods
* Sums of Squares and Nonlinear Equations
* Introduction
* Linear Programming
* The Theory of Constrained Optimization
* Quadratic Programming
* General Linearly Constrained Optimization
* Nonlinear Programming
* Other Optimization Problems

About the Author

About the author Professor Roger Fletcher completed his MA at the University of Cambridge in 1960 and his PhD at the University of Leeds in 1963. He was a lecturer at the University of Leeds from 1963 to 1969, then Principal Scientific Officer at AERE Harwell until 1973. He then joined the University of Dundee where he is Professor of Optimization and holds the Baxter Chair of Mathematics. In 1997 he was awarded the prestigious Dantzig Prize for fundamental contributions to algorithms for nonlinear optimization, awarded jointly by the Society for Industrial and Applied Mathematics and the Mathematical Programming Society. He is a Fellow of the Royal Society of Edinburgh and of the Institute of Mathematics and its Applications.

Product Details

• Paperback: 450 pages
• Publisher: Wiley; 2 edition (May 2000)
• Language: English
• ISBN-10: 0471494631
• ISBN-13: 978-0471494638
• Product Dimensions: 9 x 6 x 1 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #656,504 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

30 of 33 people found the following review helpful:

5.0 out of 5 stars Help you know what's under the hood, July 27, 2001

By 

B. H. "thinstone" (NY USA) - See all my reviews

This review is from: Practical Methods of Optimization (Paperback)

This is a very well-written book. It achieved both mathematical clearness and simplicity. I especially like the first part, unconstrained optimization. On the one hand, unconstrained optimization is very widely used. On the other hand, there isn't much content in it. Yet, there aren't many books explaining this small area clearly. This book starts with describing the structures of all methods, which gives you a sort of bird's eye view. It then devotes one chapter to each of the 3 major families of optimization methods. Comparing with another popular book, Numerical Recipes, which is orgnized by individual algorithms, this book will cerntainly gives the reader better understanding of the essence of all the algorithms. And as the name says, it's about 'practial' methods. You'll have no problem to implement the algorithms in the book and there are also many working examples to help you see how an algorithm works and help verify the implementation.

17 of 19 people found the following review helpful:

5.0 out of 5 stars Paperback reprint of 2nd Ed. from 1987, June 12, 2002

By 

J. Donahue "Elect. Eng." (Blacksburg, VA) - See all my reviews
(REAL NAME)   

This review is from: Practical Methods of Optimization (Paperback)

This is a good book from an award winning author and researcher in this subject. However, the 2000 publication date shown refers to the release of the paperback version. There is no new content since 1987 when the 2nd ed. was originally published in hardcover.

I prefer Dennis and Schnabel's _Numerical Methods for Unconstrained Optimization and Nonlinear Equations_ for Newton-derived methods in unconstrained optimization, but Fletcher's book has the added material on constrained optimization (Part 2) that makes it more complete if one wants a single reference that covers the gamut of optimization.

9 of 10 people found the following review helpful:

5.0 out of 5 stars A classic and must-have for researchers using optimization, December 15, 2004

By 

A mathematically-oriented reader (USA) - See all my reviews

This review is from: Practical Methods of Optimization (Paperback)

I recommend this book for anybody needing to learn the basics of optimization as well as a reference for people already in the field. Dr. Fletcher covers the basics, advantages, and disadvantages of optimization methods capitalizing on his long experience on the field. I find the book to be clearly written and easy to follow. Although notation is clearly explained when introduced, the author gives a notation summary at the begining of the book. This makes the book usefull as a learning as well as a reference. Although the book has not changed since the second edition, the optimization methods it describes are still the most-widely-applicable ones.