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Convex Optimization 1st Edition

4.4 out of 5 stars 33 customer reviews
ISBN-13: 978-0521833783
ISBN-10: 0521833787
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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

Book Description

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It 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: 727 pages
  • Publisher: Cambridge University Press; 1 edition (March 8, 2004)
  • Language: English
  • ISBN-10: 0521833787
  • ISBN-13: 978-0521833783
  • Product Dimensions: 7.4 x 1.6 x 9.7 inches
  • Shipping Weight: 3.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (33 customer reviews)
  • Amazon Best Sellers Rank: #70,704 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Hardcover Verified Purchase
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 [...] 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
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Format: Hardcover Verified Purchase
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.
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Format: Hardcover
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.
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Format: Hardcover
This text has lots of good examples and covers quite a bit of material. However, the proofs are very sloppy and overly complicated at best; if you're an engineer then you probably don't care about mathematical proofs but for me, and others like me, proofs reinforce concepts and reading good proofs is a great way to connecting different areas of mathematics. Examples reinforce theorems but good proofs reinforce the underlying mathematics.

In conclusion, if you're an engineer, you'll probably like this book. But for mathematicians, you might feel like I do, that this book should be titled something like "Applied Convex Optimization (for engineers)."
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Format: Hardcover Verified Purchase
This material is somewhat tangential to my research, but I learned a ton by reading it. Very well organized.

For example, here is a problem I was working on. For a given matrix A, find vectors a and b such that

1. |A| <= ab^T, (outer product) and

2. a^Tb (inner product) is a minimum. Convex Optimization showed me how to convert this into a CO problem
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By XYZ on October 9, 2011
Format: Hardcover
This book trains you to recognize convexity, gives you the associated tools, also has a few chapters on the details of the tools. You will also end up knowing what to do when your problem is not convex. Coupled with Boyd's lecture videos and slides, it is an excellent place to learn about convex optimization for an engineer.
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Format: Hardcover
The book excels in readability and style. A perfect balance on the theoretical and practical aspets of the convex optimization. As the name implies, and also as the authors put in preface, it is about recognizing, formulating, and solving convex optimization problems. Provides necessary mathematical background in the first part---not as deeply as a gradute level convex analysis book---and therefore helps reader build a working knowledge. If something is not covered in this part but essential for a working knowledge, then it is in the appendices for sure. Provides a wealth of examples, exercises, and applications. Perfect for self-study as well as classroom use.
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