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Convex Analysis (Princeton Landmarks in Mathematics and Physics) Paperback – December 23, 1996

ISBN-13: 000-0691015864 ISBN-10: 0691015864

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Product Details

  • Series: Princeton Landmarks in Mathematics and Physics
  • Paperback: 472 pages
  • Publisher: Princeton University Press (December 23, 1996)
  • Language: English
  • ISBN-10: 0691015864
  • ISBN-13: 978-0691015866
  • Product Dimensions: 8.9 x 6 x 1 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #233,725 in Books (See Top 100 in Books)

Editorial Reviews

Review

"This book should remain for some years as the standard reference for anyone interested in convex analysis."--J. D. Pryce, Edinburgh Mathematical Society

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Customer Reviews

4.1 out of 5 stars
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See all 8 customer reviews
It just takes way too much time. c) The book is about convex analysis, not convex geometry.
Zach
It is probably the best reference book although it is tough to read from the beginning untill the end.
Bernardo Pagnoncelli
This is the most important and influential book ever written on convex analysis and optimization.
Academic

Most Helpful Customer Reviews

6 of 6 people found the following review helpful By Zach on July 25, 2013
Format: Paperback Verified Purchase
In a nutshell, an exceptional book, ideal for reference (completeness and organization stands out), but also excellent for self-studying too! In fact, the last part came as a pleasant surprise to me.

You just need to understand that
a) you would rather have previous exposition to abstract mathematics (otherwise I doubt it is fit for you),
b) The first few sections quickly introduce you to convex analysis, but the book is huge and it is extremely ambitious to try to read it from cover to cover. It just takes way too much time.
c) The book is about convex analysis, not convex geometry. He obviously gives all needed information about the geometry, but don't expect to find fancy figures and illustrations (it has none), plus it was written in the 60s and illustrations back then were awful anyway.
d) The book contains theoretical results pertaining to convex optimization, and is certainly written, in large, with that in mind. But remember, it is about the theory, not about the algorithms etc. You need it if you need to get a profound knowledge on the theoretical aspects of convexity.

He explains and motivates the introduction of every new definition, and although he is very meticulous in the proofs, most of them are really simplified and well presented. He actually breaks most results into small theorems, and he progressively builds upon previous results to prove the more complex theorems. This helps keep proofs really short and intuitively appealing.

TARGET AUDIENCE
Remarkable clarity and depth in the exposition. However, as the author does mention, this book requires mathematical maturity to understand. The reader would rather have even a superficial exposition to abstract mathematics.
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5 of 5 people found the following review helpful By Academic on October 21, 2009
Format: Paperback
This is the most important and influential book ever written on convex analysis and optimization. Based on the works of Fenchel and other mathematicians from the 50s and early 60s (such as the Princeton school), Rockafellar takes the subject to a new level, with a deep and comprehensive synthesis, focused primarily on a definitive development of duality theory, and of the convex analysis that supports it. This is the place to start if you are looking for a result on the theory and convex sets and functions, or duality theory; the book is comprehensive. This is not an easy book to read, and it would benefit from illustrations and exercises (it has none). However, its value and profound influence on the field are hard to overestimate.
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3 of 4 people found the following review helpful By Bernardo Pagnoncelli on May 9, 2007
Format: Paperback
This book is a classic. It is probably the best reference book although it is tough to read from the beginning untill the end. The style is heavy and you need strong mathematical background to understand it.

Anyway, if you need a result on convex functions or convex analysis it is very likely that you will find it in ths book.
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0 of 2 people found the following review helpful By George Thomas on March 26, 2012
Format: Paperback
A serious piece, but actually very readable. Its packed with precious jewels if you already have an exposure to convexity.
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