Numerical Optimization (Hardcover)

by Jorge Nocedal (Author), Stephen Wright (Author) "People optimize. Airline companies schedule crews and aircraft to minimize cost..." (more)
Key Phrases: linear conjugate gradient method, basic feasible point, secant equation, Hessian of the Lagrangian, Lagrangian Hessian (more...)

Editorial Reviews

Review
MMOR Mathematical Methods of Operations Research, 2001: "The books looks very suitable to be used in an graduate-level course in optimization for students in mathematics, operations research, engineering, and others. Moreover, it seems to be very helpful to do some self-studies in optimization, to complete own knowledge and can be a source of new ideas.... I recommend this excellent book to everyone who is interested in optimization problems." --This text refers to the Hardcover edition.

Product Description
NUMERICAL OPTIMIZATION presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.

Drawing on their experiences in teaching, research, and consulting, the authors have produced a textbook that will be of interest to students and practitioners alike. Each chapter begins with the basic concepts and builds up gradually to the best techniques currently available.

Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the area.

Above all, the authors have strived to produce a text that is pleasant to read, informative and rigorous--one that reveals both the beautiful nature of the discipline and its practical side.

Product Details

• Hardcover: 656 pages
• Publisher: Springer (April 28, 2000)
• Language: English
• ISBN-10: 0387987932
• ISBN-13: 978-0387987934
• Product Dimensions: 9.5 x 7.3 x 1.5 inches
• Shipping Weight: 2.7 pounds
• Average Customer Review: 4.6 out of 5 stars See all reviews (14 customer reviews)
• Amazon.com Sales Rank: #775,551 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

25 of 27 people found the following review helpful:

4.0 out of 5 stars Nice but could be better!, April 14, 2000

By A Customer

This book by Nocedal and Wright has several attractive features. For one, it is probably the most "state-of-the-art" of the existing texts in optimization and as such covers most of the modern methods. It also has a nice section on LP (simplex as well as interior point methods) for someone interested in a course on optimization as opposed to NONLINEAR optimization (which is what I was looking for). Another strength is that it covers many of the algebra-related details very well. My only major complaint is that it seems to not get into any of the methods designed specifically for convex programs - these while admittedly less general are often very powerful. For example, there is NO mention even of Geometric Programming which has wide application in design. The convex simplex method also isn't mentioned anywhere. Finally,I wonder why there is no mention of the generalized reduced gradient (GRG) method.

All in all, a good book to own I think...

12 of 14 people found the following review helpful:

5.0 out of 5 stars Teaches good mathematical programming techniques, April 13, 2002

By	Sunanda Dutta "kolikata" (Hoboken, NJ) - See all my reviews (REAL NAME)

The book does a very good job in teaching non-discrete mathematical programming techniques. But, it is not an introductory book. The reader is supposed to know linear algebra and numerical analysis to a certain extent. Most of the modern techniques are presented, but the layout is a little chaotic- the sequence of subjects could be made better. So, I would have preferred to give it 4.5 stars (which is impossible). However, that does not take away the fact that the book is excellent. I have used it primarily for modelling financial portfolios, and I am sure it can be used as a guide for other applications.

Conclusion: A little difficult, but well worth the time and money involved

9 of 10 people found the following review helpful:

5.0 out of 5 stars Outstanding reference, July 16, 2006

By	wiredweird "wiredweird" (Earth, or somewhere nearby) - See all my reviews (TOP 100 REVIEWER)

Within the range that this intends to cover, it is an outstnading reference. The first two chapters lay out the mathematical preliminaries, and get the book off to a fast start. The next four chapters discuss basic classes of algorithms for nonlinear optimization and choices of stopping criteria. This includes conjugate gradient methods adapted from the CG method for solving linear systems - since, in nearly all cases, non-linear optimization breaks down into iterations over locally linear approximations.

The emphasis thoughout is on practical algorithms and efficient computation. First and second derivatives are used heavily throughout this book, but symbolic differentiation of the nonlinear functions is usually unavailable. As a result, significant emphasis goes into approximation techniques, and into the common cases of sparse systems. Despite its heavily mathematical orientation, this really is a book about the practicalities of computation.

A bit further on, Nocedal and Wright get to the topic that brought me to this book in the first place: nonlinear least squares. As always, the presentation is clear but very dense. Other topics follow, including solutions of nonlinear equations (i.e. minimizing the error in approximating the exact solution), simplex and polynomial-order techniques for linear systems, and more.

This is a book for someone who's completely at home with differential calculus and linear algebra, and who's willing to spend time extracting the full meaning from terse descriptions. It's also for a reader who is comfortable translating dense notation into working numerical code - not a task to be undertaken lightly. That reader will be rewarded with wide-ranging and very practical discussions of many problems and the techniques used for each. As it says in the introduction, this doesn't address the whole world of optimization problems - combinatorics, discrete problems, and jagged search spaces are not the subject here. If, however, this book touches on your topic, you'll find it handled very well. This has my highest recommendation.

//wiredweird