Global Optimization Using Interval Analysis (Pure and Applied Mathematics) [Hardcover]

Hansen (Author)

Book Description

ISBN-10: 0824786963 | ISBN-13: 978-0824786960 | Publication Date: July 21, 1992 | Edition: 1

Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.

--This text refers to an alternate Hardcover edition.

Editorial Reviews

Review

I wholeheartedly endorse this important new volume, and recommend its serious study by all who are concerned with global optimization.

Ramon Moore, Professor Emeritus of Computer and Information Science, Department of Mathematics, The Ohio State University, Columbus, U.S.A.
--This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 256 pages
• Publisher: CRC; 1 edition (July 21, 1992)
• Language: English
• ISBN-10: 0824786963
• ISBN-13: 978-0824786960
• Product Dimensions: 9 x 6.2 x 0.9 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #8,552,340 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

5.0 out of 5 stars Are you computing reliably yet?, April 28, 2004

By 

Nathan T Hayes (Minneapolis, MN United States) - See all my reviews

This review is from: Global Optimization Using Interval Analysis: Revised And Expanded (Pure and Applied Mathematics (M. Dekker)) (Hardcover)

With the world becomming an ever increasingly digital and technological place, it sometimes makes me uneasy to think of how many times in a day we put our lives at the mercy of computers that rely on floating-point computations. Did you know it is possible to get different results by simply changing the order in which floating-point terms are computed? We've all heard about the NASA spacecraft that was lost because two programmers were not using the same units when writing the navigation software. But this is an example of a familliar and ubiquitous problem: human error. Much more insidious, and much less recognized and understood, are the tiny rounding errors that occur all around us in practically every digital and electronic device we come in contact with. Many trains, planes and automobiles have digital circuits or software that use floating-point computations. Innovative medical technologies use sophisticated software and numerical computations. All of these systems affect our daily lives and are susceptible to the rounding errors and innacuracies of floating-point computations. The Patriot Missile failure is a dramatic example of how the accumulation of small floating-point errors resulted in a very serious problem that could have involved life and death.

With this book, Eldon and Bill provide a smashingly good resource for anyone interested in performing reliable computations on a computer by using interval analysis. Perhaps the best quality of the book is the structure and narrative. It starts simple, with the basics, by describing the problems of floating-point computations and then introducing simple interval arithmetic. Successive chapters introduce linear equations, inequalities and Taylor expansions. Further in, more difficult probelms are introduced and tackled: nonlinear equations and systems, consistencies and global optimization. With interval analysis, it is possible to rigorously bound all error in a complex computation, guaranteeing an accurate result. Even if there is no solution to the problem, intervals will figure it out and report an "empty" solution. In short, by using intervals as presented in this book, computing can be done reliably.

This book should satisfy the most eager and advanced reader who is looking to learn and apply interval analysis to real-world problems; but the first several chapters are also simple enough to provide a curious layperson with insight into how interval analysis works and why it is so desperately needed. My only criticisms of the book are that the notation sometimes gets complex and requires careful reading; and I wish the algorithms were outlined in psuedo-code instead of numbered lists. But overall, I find this book to be an excellent resource and a very handy reference manual: no longer do I have to sift through piles of whitepapers downloaded from the internet. "Global Optimization Using Interval Analysis, Second Edition" is always sitting on my desk, just an arm's reach away.

2 of 2 people found the following review helpful:

4.0 out of 5 stars Who said you couldn't minimize any C^2 function?, June 2, 2001

By 

S. Lolle (Denmark) - See all my reviews

This review is from: Global Optimization Using Interval Analysis (Pure and Applied Mathematics) (Hardcover)

A splendid book on a splendid - but often overseen - subject in nonlinear programing. Can be recommended for advanced students in mathematics. The book describes in great detail without getting boring how a function of n variables is being minimized (globaly) using interval arithmetics. The book builds on an article he wrote back in the beginning of the '80s and does a much better job than the article! The algorithm presented does guarantee to find the global minimum (minima). It does not spend long time searching between thousands of other stationary points. It seems that the future of optimisation might depend heavily on interval arithmetics. Let's hope that more software will be devoloped in the future, so that this topic will become more common!

Even though the book has - unfortunately - quite a few(mathematical) typing errors they don't mess up the over all impression!