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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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
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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Most Helpful Customer Reviews
26 of 26 people found the following review helpful
Format:Hardcover|Amazon 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. 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.
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.
20 of 21 people found the following review helpful
Format:Hardcover
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
23 of 26 people found the following review helpful
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.
Most Recent Customer Reviews
5.0 out of 5 stars
Great book
It is a well thought book and, moreover, there are the Convex Optimization course available in Youtube. Read more
Published 16 days ago by Owl
3.0 out of 5 stars
How to actually solve it please
I want to like this book. But please tell me where is anything actually solved? Browsing through the book to decide if I should work my way through it or not, it looks for all the... Read more
Published 4 months ago by Jeffrey M. Lee
5.0 out of 5 stars
it is good
anyway, it is good. It is a classic book in communication and signal processing area. The book is quite new.
Published 5 months ago by Songtao Lu
5.0 out of 5 stars
brand new book, in good quality~
Convex Optimization
It's a new book and the quality of the book is good. It is helpful for my study of Convex Optimization in UCLA.
It's a new book and the quality of the book is good. It is helpful for my study of Convex Optimization in UCLA.
Published 15 months ago by Suki
5.0 out of 5 stars
Great Book
This book trains you to recognize convexity, gives you the associated tools, also has a few chapters on the details of the tools. Read more
Published 19 months ago by XYZ
5.0 out of 5 stars
Convexoptimization reference
This book can be considered as a reference in convex optimization.
It is clearly written with a lot of examples.
It is clearly written with a lot of examples.
Published on April 5, 2011 by Jerome Gilles
5.0 out of 5 stars
Wonderful Text on optimization
This is an excellent text on optimization. The pdf version is free on the net. First I got the pdf version, I like the writing style and the way authors have described the... Read more
Published on September 26, 2010 by A. N. Bajwa
5.0 out of 5 stars
Readable!
Well written and intuitive. Check out the online copy by following the link from the convex programing page on Wikipedia.
Published on November 11, 2009 by Prof Wollongong
1.0 out of 5 stars
ONE WORD: SKIMPY!!!
Save your money and consult the free online edition, if you must.
I needed this book for a class, but if you have the option, look for a better and more complete book. Read more
I needed this book for a class, but if you have the option, look for a better and more complete book. Read more
Published on November 12, 2008 by Pete
5.0 out of 5 stars
An excellent introduction to convex optimization models
Boyd's and Vanderbergue's book offers a lot: good intuition to theoretical convex optimization and its tools, sophisticated descriptions of many convex optimization applications,... Read more
Published on November 5, 2008 by Academic
Citations (learn more)
This book cites 76
books:
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66
books
cite this book:
See all 66 books citing this book
- Handbook of Global Optimization Volume 2 (Nonconvex Optimization and Its Applications (closed)) by Panos M. Pardalos in Back Matter
- Fundamentals of Convex Analysis (Grundlehren Text Editions) by Jean-Baptiste Hiriart-Urruty in Back Matter
- Functional Analysis by L. V. Kantorovich in Back Matter
- Convex Analysis (Princeton Landmarks in Mathematics and Physics) by Ralph Tyrell Rockafellar in Back Matter
- Introduction to Optimization (Translations Series in Mathematics and Engineering) by Boris T. Polyak in Back Matter
See all 76 books this book cites
- Learning Theory: 19th Annual Conference on Learning Theory, COLT 2006, Pittsburgh, PA, USA, June 22-25, 2006, Proceedings (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence) by Hans Ulrich Simon on 4 pages
- Convex Optimization & Euclidean Distance Geometry by Jon Dattorro in Front Matter (1), Front Matter (2), and Back Matter
- MIMO Wireless Communications by Ezio Biglieri on page 78, page 135, and Back Matter
- Actuator Saturation Control (Automation and Control Engineering) by Vikram Kapila on page 105, and page 185
- Space-Time Processing for MIMO Communications by Alex Gershman on page 313, and page 314
See all 66 books citing this book
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