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Practical Methods of Optimization, by R. Fletcher
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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.
- Sales Rank: #1308317 in Books
- Published on: 2000-05
- Original language: English
- Number of items: 1
- Dimensions: 9.11" h x .98" w x 6.06" l, 1.43 pounds
- Binding: Paperback
- 456 pages
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.
Most helpful customer reviews
8 of 8 people found the following review helpful.
Invaluable insight
By K. Dixon
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.
4 of 4 people found the following review helpful.
Indispensable
By penguin
I'm a software engineer with only a BS in computer science who worked in a team translating a Matlab prototype of in-house non-linear multilevel optimizer to C++. I had no theoretical background in optimization and, during the time I was working on the project, I did not have (or bother) a chance to sit and study the subject. When I finally did and found this book, all the thick and widespread clouds over my head that persisted for years started clearing up immediately. This book may not cover the state of the art algorithms or theory but is a great place to start. It gives us a solid foundation before moving on to more specialized or theoretical topics on our own (or motivate us enough to go back to school!).
22 of 24 people found the following review helpful.
Paperback reprint of 2nd Ed. from 1987
By J. Donahue
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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