Convex Optimization (Hardcover)

~ Stephen Boyd (Author), Lieven Vandenberghe (Author) "In this introduction we give an overview of mathematical optimization, focusing on the special role of convex optimization..." (more)
Key Phrases: quasiconvex optimization problem, backtracking parameters, quadratically convergent phase, Monte Carlo, The A-optimal (more...)

Editorial Reviews

Review

"Boyd and Vandenberghe have written a beautiful book that I strongly recommend to everyone interested in optimization and computational mathematics: Convex Optimization is a very readable and inspiring introduction to this modern field of research...The book will be accessible not only to mathematicians but also to researchers and students who want to use convex optimization in applied fields like engineering, computer science, economics, statistics, or others. I recommend it as one of the best optimization textbooks that have appeared in the last years."
Mathematical Methods of Operations Research


"...this concisely writen book is useful in many regards: as a primary textbook for convex optimization with engineering applications or as an alternate text for a more traditional course on linear or nonlinear optimization."
Journal of the American Statistical Association, Hans-Jakob Luethi, Swiss Federal Institute of Technology Zurich


"The book by Boyd and Vandenberghe reviewed here is one of ... the best I have ever seen ... it is a gentle, but rigorous, introduction to the basic concepts and methods of the field ... this book is meant to be a 'first book' for the student or practitioner of optimization. However, I think that even the experienced researcher in the field has something to gain from reading this book: I have very much enjoyed the easy to follow presentation of many meaningful examples and suggestive interpretations meant to help the student's understanding penetrate beyond the surface of the formal description of the concepts and techniques. For teachers of convex optimization this book can be a gold mine of exercises."
MathSciNet

Product Description

Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

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Product Details

• Hardcover: 730 pages
• Publisher: Cambridge University Press (March 8, 2004)
• Language: English
• ISBN-10: 0521833787
• ISBN-13: 978-0521833783
• Product Dimensions: 9.8 x 7.4 x 1.5 inches
• Shipping Weight: 3.8 pounds (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (8 customer reviews)
• Amazon.com Sales Rank: #221,326 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

20 of 22 people found the following review helpful:

5.0 out of 5 stars Excelent reference both for theory and practice, March 2, 2006

By	J. J. Arrieta-Camacho "Wannabe Rocket Scientist" (Pittsburgh, PA USA) - See all my reviews (REAL NAME)

The book provides sound theoretical basis in a non-intimidating way. It also presents many examples that help the reader understand and relate his or her specific needs to general convex optimization problems. I think this book is a really good compromise between theory and practice: it can please the more mathematics-oriented with proofs, definitions, and bibliography; as well as the more application-oriented with examples, implementations, and heuristics. The authors have been very generous in allowing the free download of the full book from their website.

4 of 4 people found the following review helpful:

5.0 out of 5 stars The way to go for introducing optimization, May 30, 2008

By	A. Gustafson - See all my reviews (REAL NAME)

Quite simply, this is a wonderful text. Coupling this with Boyd's course at Stanford (the lecture videos, HWs, etc. are all available for free online), you're bound to learn quite a lot about optimization. But most importantly, you'll have an idea of when you can actually apply convex optimization to solve a problem that comes up in your particular field.

My reasoning in giving it such praise is my preference for the rather unusual methodology it takes in introducing you to optimization. Most books I have seen on linear programming or non-linear programming tackle a few standard problems, introduce what is necessary in terms of definitions and proofs, and then focus on the algorithms that solve these standard problems (conjugate gradient et. al.), how they work, their pitfalls, etc. While this is undoubtedly useful material (which Boyd does cover for a good deal in the final chapters), the simple fact of the matter is these algorithms are available as standard methods in optimization packages (which are abstracted from the user), and unless you are actually going into developing, implementing and tweaking algorithms, this quite honestly is useless.

What this book attempts to do, and does very well in my opinion, is to teach you to recognize convexity that's present in problems that are first glance appear to be so incredibly removed from optimization that you might never consider it. This book spends the first 100 pages or so just devoted to building a "calculus" of convexity, if you will, so that you know through what operations convexity is preserved, and you develop intuition as to the potential to use convex optimization in problems in your particular field or application. As such, the first part of the books is focused on building up the skill set, the second part to applications of convex programming, and only the third to the actual algorithms.

A word of warning: some of the explanations (especially in Chapter 4 which focuses on types of convex programs and equivalence of programs) are very general, which won't be satisfying to certain readers who need solid examples to reinforce the concepts. Also, a lot of the material can be quite challenging, requiring a bit of mental gymnastics. However, if you are accompanying your study with the problems at the end of each chapter, you're certain to get practice and demystify the concepts.

In sum, all things considered, a great text.

6 of 7 people found the following review helpful:

4.0 out of 5 stars A very good starting point for convex optimization, August 5, 2008

By	Nikolaos Vasiloglou "just an engineer" (Georgia Tech) - See all my reviews

I think this is the best book for getting into optimization. It's simple with many examples and figures. Excellent choice for engineers, mathematicians might find it incomplete, but what can we do, that's life. I think the interior point section could have had more, but it is still ok. The next step after this book is Nemirovski's book "Lectures on Modern Convex optimization". You can download it for free from his website http://www2.isye.gatech.edu/~nemirovs/ along with many other notes. Nemirovski's book is very complete and has very modern ideas new to many engineers. But as I said Boyd's book is where you should start from. From an engineer's perspective I believe Boyd's book is much more easy to read and understand than Bertseka's book Convex Analysis and Optimization. I also appreciate Boyd's courtesy to have his book available on-line for free. I bought the book after downloading it because it is worth its price. Try also another book coming from Stanford, which is more specialized Convex Optimization & Euclidean Distance Geometry, also available on-line