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Practical Methods of Optimization Paperback – May 1, 2000

ISBN-13: 978-0471494638 ISBN-10: 0471494631 Edition: 2nd

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Product Details

  • Paperback: 456 pages
  • Publisher: Wiley; 2 edition (May 2000)
  • Language: English
  • ISBN-10: 0471494631
  • ISBN-13: 978-0471494638
  • Product Dimensions: 9.1 x 5.9 x 1.2 inches
  • Shipping Weight: 1.4 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: #567,671 in Books (See Top 100 in Books)

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.

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32 of 35 people found the following review helpful By B. H. on July 27, 2001
Format: 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.
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20 of 22 people found the following review helpful By J. Donahue on June 12, 2002
Format: 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.
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13 of 14 people found the following review helpful By A mathematically-oriented reader on December 15, 2004
Format: 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.
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6 of 6 people found the following review helpful By K. Dixon on June 28, 2008
Format: Paperback Verified Purchase
This book is a great mix of insight and rigor. The text is mixed with mathematical propositions/proofs and a lively writing style. The proofs aren't gratuitous, as opposed to most texts, but meant to build insight and demonstrate properties of algorithms. After each proof Fletcher doesn't meander in the weeds of the math, but he takes a step back and provides insight about WHAT this means for a particular algorithm.

Fletcher then highlights the algorithms by bringing in his own experience and provides insight on how the algorithms work on real problems, not just what the theory says. He writes that many algorithms, including several developed by him, are inferior to other variants on real-world problems. (Fletcher is the "F" in BFGS, DFP, and Fletcher-Reeves conjugate gradient.)

This coupling of mathematical rigor with candid insight makes this book invaluable.

On the negative side, I have found (as others have noted) a few typos, including a couple obvious ones in the pseudocode. This book is meant "to teach a man to fish," not "give a man a fish." So, if you're looking for something like Numerical Recipes that gives you verbatim software to type into your computer, then Fletcher's book isn't for you. However, after digesting Fletcher's math and insight, I have been able to reduce the computation of my (formerly NR-based) codes by an order of magnitude on some standard-battery optimizations.
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