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Convex Analysis (Princeton Landmarks in Mathematics and Physics)

4.1 out of 5 stars 8 customer reviews
ISBN-13: 000-0691015864
ISBN-10: 0691015864
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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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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: 6 x 1.1 x 9 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: #719,502 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback Verified Purchase
In a nutshell, an exceptional book, ideal for use as a 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.

PhD Candidates conducting theoretical research could definitely learn a great deal about writing elegant and good math from this book.

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.
c) The book is about convex ANALYSIS, NOT CONVEX GEOMETRY. It (intentionally) does not focus on the geometric interpretation of convexity and for a good reason. Many convex settings involve multiple dimensions (e.g. thousands for convex optimization problems). A geometric account is more intuitive but does not safely and readily extend to multiple dimensions, where intuition is lost or becomes error prone. That is where analysis shines, as it abstracts the geometric intuition into algebraic relations and properties. So don't expect to find fancy figures and illustrations (it has none).
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 to gain profound knowledge on the theoretical aspects of convexity. If you need to focus on convex optimization see e.g. the book from Stephen Boyd on Convex Optimization (also available for free on his website).
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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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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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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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