Practical Optimization [Paperback]

Philip E. Gill (Author), Walter Murray (Author), Margaret H. Wright (Author)

Book Description

Publication Date: January 28, 1982 | ISBN-10: 0122839528 | ISBN-13: 978-0122839528

This book is designed to help problem solvers make the best use of optimization software--i.e., to use existing methods most effectively whenever possible, and to adapt and modify techniques for particular problems if necessary. The contents of this book therefore include some topics that are essential for all those who wish to solve optimization problems. In addition, certain topics are treated that should be of special interest in most practical optimization problems. For example, advice is given to users who wish to take an active role in formulating their problems so as to enhance the chances of solving them successfully, and to users who need to understand why a certain method fails to solve their problem.

Editorial Reviews

From the Back Cover

Numerical optimization and parameter estimation are essential tools in a wide variety of applications, such as engineering, science, medicine, sociology and economics. For these optimization techniques to be exploited effectively, problem solvers need to be fully informed of the scope and organization of software for both the specialist and non-specialist; the underlying numerical methods; the aspects of problem formulation that affect performance; the assessment of computer results and the resolution of difficulties that may occur during the solution process.
These topics form the basis of the organization of Practical Optimization. Much of the material about the estimation of results and the preparation of the problem has not been previously published. The book contains a description of methods for numerical optimization to a level which should make it a useful course text. It is intended that the book should be self-contained. Consequently, those elements of calculus, linear algebra and numerical analysis pertinent to optimization are reviewed in the opening chapters. This is the first book on optimization which discusses not only the methods but also the analysis of computed results and the preparation of problems before solution.
This volume will prove invaluable to those in industry, university and research establishments who are actively engaged in solving optimization problems and to those who are potential users of optimization software.

Product Details

• Paperback: 420 pages
• Publisher: Emerald Group Publishing Limited (January 28, 1982)
• Language: English
• ISBN-10: 0122839528
• ISBN-13: 978-0122839528
• Product Dimensions: 9.2 x 8.2 x 0.9 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 3.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,001,370 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

20 of 24 people found the following review helpful:

3.0 out of 5 stars Was good in its day, March 13, 2001

By 

Mark Leifer (Boulder, CO) - See all my reviews
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This review is from: Practical Optimization (Paperback)

After some initial use, this book sat unused in my library for many years. We were reacquainted recently when I needed help in solving a nonlinear optimization problem with some tricky aspects.

Rather than being a cookbook of optimization algorithms, it is a thoughtful text about optimization problems and the algorithms used to solve them written by experienced researchers who contributed algorithms for the renowned Numerical Algorithms Group (NAG). It leads one through the classification tree of algorithms (much as you'd do at, e.g., NIST's Guide to Available Mathematical Software), but with chapters and sections devoted to each category or subcategory so you can fully understand the approach and its behavior in detail. This book therefore complements the more typical algorithm- and package- (e.g., Matlab) oriented treatments.

Strengths: a) Good comparisons of similar methods with advice on when to use each. b) Nice discussions, brought alive by many graphs and simple but subtle example problems to illustrate each algorithm and its idiosyncracies.

Weaknesses: a) Sections don't stand alone. I found myself flipping back to early chapters where certain formalisms are introduced. b) The book is dated. The 70's approaches to solving a constrained problem by using penalty functions with a series of unconstrained optimizations have largely been supplanted by new methods based on the Kuhn-Tucker equations. c) There is no coverage, obviously, of other important modern techniques (simulated annealing, genetic algorithms, neural nets) developed after the book was written in 1981.

In summary: It was good in its day, and may still be helpful in understanding the classic algorithms and choosing the best. You'll need to look elsewhere, however, for a modern treatment.

5 of 5 people found the following review helpful:

4.0 out of 5 stars Old, but still helpful, July 13, 2004

By 

wiredweird "wiredweird" (Earth, or somewhere nearby) - See all my reviews
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This review is from: Practical Optimization (Paperback)

This is a clear, useable introduction to basic techniques for numerical optimization. It addresses the classic kinds of optimization targets: differentiable (mostly) and unimodal (mostly), with or without constraints of various kinds.

Maybe that sounds a little naive and optimistic by today's standards. It still describes a large class of useful problems, though, and may help with end-stage refinement of local optima found other ways. Even genetic optimization algorithms can benefit from classical techniques - a Lamarckian mutation operator may actively seek local improvement instead of relying purely on random perturbation.

Gill covers a variety of techniques, using the first or second derivatives or discrete approximations. He also presents a simplex technique, not to be confused with the simplexes used in linear optimizations. Throughout, he puts strong emphasis on numerical stability and on the relative strengths and weaknesses of each approach, all the way back to the linear systems that approximate each step of the analysis.

It's not a recent book, but that is part of its value. Many of its techniques are almost lost. They have been included by specialists into canned analysis tools, hidden from sight, and forgotten even by the people who use them. I often need to go back to these basics, and very few more recent books are as clear or complete, over this book's range of topics.

Gill has written clearly enough for a careful programmer to implement the algorithms. There is not much here for theoreticians or cut&paste hackers, but it's a useful reference for someone willing to put the time into understanding.

//wiredweird

2 of 2 people found the following review helpful:

4.0 out of 5 stars old but still good book, December 10, 2008

By 

J. Schumann - See all my reviews
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This review is from: Practical Optimization (Paperback)

This book is really good to read and gives a great overview and discussion of (by then) important techniques for unconstrained/constrained optimization methods together with a lot of practical eye-openers. It covers a lot of different variants and their interrelation and thus helped me tremendously to understand and structure the field. Does not contain code.
Still my favorite book on nonlinear optimization.