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内容説明
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 book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. 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.
著者について
Stephen Boyd received his PhD from the University of California, Berkeley. Since 1985 he has been a member of the Electrical Engineering Department at Stanford University, where he is now Professor and Director of the Information Systems Laboratory. He has won numerous awards for teaching and research, and is a Fellow of the IEEE. He was one of the co-founders of Barcelona Design, and is the co-author of two previous books Linear Controller Design: Limits of Performance and Linear Matrix Inequalities in System and Control Theory.
Lieven Vandenberghe received his PhD from the Katholieke Universiteit, Leuven, Belgium, and is a Professor of Electrical Engineering at the University of California, Los Angeles. He has published widely in the field of optimization and is the recipient of a National Science Foundation CAREER award.
Lieven Vandenberghe received his PhD from the Katholieke Universiteit, Leuven, Belgium, and is a Professor of Electrical Engineering at the University of California, Los Angeles. He has published widely in the field of optimization and is the recipient of a National Science Foundation CAREER award.
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私は研究上、半正定値計画法を理論的にも実際の数値計算上もよく使うのですが、常々参考にさせてもらっている教科書です。
内容は充実していますし、廉価だし文句なしで「とりあえず買っておけ」って教科書です。
もちろん、あくまでも入門書なので、計算複雑性その他、カバーしきれていないところが多々ありますが、
とりあえず、自分の仕事で凸最適化を使うなら買っておいて損はぜったいしません。
海外では、この分野で一番の標準的な教科書ということになっております。
内容は充実していますし、廉価だし文句なしで「とりあえず買っておけ」って教科書です。
もちろん、あくまでも入門書なので、計算複雑性その他、カバーしきれていないところが多々ありますが、
とりあえず、自分の仕事で凸最適化を使うなら買っておいて損はぜったいしません。
海外では、この分野で一番の標準的な教科書ということになっております。
2 人中、1人の方が、｢このレビューが参考になった｣と投票しています。
形式:ハードカバー
凸最適化の基礎理論と最適化手法をきっちり扱った分厚い入門書．本書の存在はその昔に著者の講演を聞いたときから知っていたけど買ったのは最近．分厚い教科書一冊でカバーできるほど狭い分野じゃないので載っていない話題も多々ありますが，「オーソドックスな知識を得たい」とか「理論的に何が可能なのか知りたい」という人が，「どれか一冊」という基準で選ぶなら僕が知っている中ではダントツで本書です．ここ数年で当り前になった膨大なデータの分析やそれに基づいた戦略作りのときに，チームに数学者を入れると色々できることがよくわかります．仮に本書のきちんとした和訳が出版されたならば，日本人著者による同じ話題の教科書の半分は図書館から捨ててもよいでしょうね．
お腹いっぱいなので半分ほどしか読んでいませんし，演習問題は解いてはいませんが，アメリカの有名(らしい)な学者の本らしく至れり尽くせりです．まず，エンジニアの僕が新幹線の中で読む気になるほど分かりやすいし，もちろんちゃんと証明も載っています．わかりやすいといっても，学生時代に結構数学をやっていた人にとってであって，学部1年の線形代数や微積分で挫折した人には無理でしょうけど．また，間違いらしきものは僕が読んだ範囲では見つかりませんでした．
あと，例題と演習問題も秀逸です．理論の最もコアな部分は本論で，他分野との関連や応用面の意義や本論では書ききれない面白い性質などは例題と演習問題でという形です．
お腹いっぱいなので半分ほどしか読んでいませんし，演習問題は解いてはいませんが，アメリカの有名(らしい)な学者の本らしく至れり尽くせりです．まず，エンジニアの僕が新幹線の中で読む気になるほど分かりやすいし，もちろんちゃんと証明も載っています．わかりやすいといっても，学生時代に結構数学をやっていた人にとってであって，学部1年の線形代数や微積分で挫折した人には無理でしょうけど．また，間違いらしきものは僕が読んだ範囲では見つかりませんでした．
あと，例題と演習問題も秀逸です．理論の最もコアな部分は本論で，他分野との関連や応用面の意義や本論では書ききれない面白い性質などは例題と演習問題でという形です．
Amazon.com で最も参考になったカスタマーレビュー (beta)
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19 人中、19人の方が、｢このレビューが参考になった｣と投票しています。
The way to go for introducing optimization
2008/5/30
形式:ハードカバー|Amazonが確認した購入
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.
24 人中、22人の方が、｢このレビューが参考になった｣と投票しています。
Excelent reference both for theory and practice
2006/3/2
形式:ハードカバー
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.
15 人中、14人の方が、｢このレビューが参考になった｣と投票しています。
A very good starting point for convex optimization
2008/8/6
形式:ハードカバー
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
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