Numerical Optimization (Springer Series in Operations Research and Financial Engineering) [Hardcover]

Jorge Nocedal (Author), Stephen Wright (Author)

Book Description

ISBN-10: 0387303030 | ISBN-13: 978-0387303031 | Publication Date: July 27, 2006 | Edition: 2nd

Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

Editorial Reviews

Review

Aus den Rezensionen zur 2. Auflage: "… Der Aufbau folgt ... vielen Standardwerken über nichtlineare Optimierung. ... Das Buch bietet eine detaillierte und gut lesbare Übersicht über den aktuellen Stand der Forschung in nichtlinearer Optimierung. Viele Aufgaben unterschiedlichen Schwierigkeitsgrades bieten auch den Lernenden eine nützliche Unterstützung. Insgesamt halte ich dieses Werk als Grundlage für eine Lehrveranstaltung über nichtlineare Optimierung hervorragend geeignet und habe es bereits selbst erfolgreich eingesetzt." (F. Rendl, in: IMN - Internationale Mathematische Nachrichten, 2008, Vol. 62, Issue 208, S. 69 f.)

From the Back Cover

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. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. 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 field. 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: 686 pages
• Publisher: Springer; 2nd edition (July 27, 2006)
• Language: English
• ISBN-10: 0387303030
• ISBN-13: 978-0387303031
• Product Dimensions: 9.3 x 7.1 x 1.5 inches
• Shipping Weight: 2.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (14 customer reviews)
• Amazon Best Sellers Rank: #83,913 in Books (See Top 100 in Books)
  • #29 in Books > Professional & Technical > Professional Science > Physics > System Theory
  • #60 in Books > Business & Investing > Management & Leadership > Operations Research

Customer Reviews

Most Helpful Customer Reviews

29 of 32 people found the following review helpful:

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

By A Customer

This review is from: Numerical Optimization (Hardcover)

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...

14 of 16 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)   

This review is from: Numerical Optimization (Hardcover)

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

13 of 16 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
(HALL OF FAME REVIEWER)    (TOP 500 REVIEWER)   

This review is from: Numerical Optimization (Hardcover)

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