Convex Optimization

Convex Optimization

Convex Optimization

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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3 comments

  1. 33 of 35 people found the following review helpful
    5.0 out of 5 stars
    The way to go for introducing optimization, May 30, 2008
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    This review is from: Convex Optimization (Hardcover)
    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.

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  2. 24 of 25 people found the following review helpful
    4.0 out of 5 stars
    A very good starting point for convex optimization, August 5, 2008
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    This review is from: Convex Optimization (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 […] 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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  3. 24 of 27 people found the following review helpful
    5.0 out of 5 stars
    Excelent reference both for theory and practice, March 2, 2006
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    This review is from: Convex Optimization (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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