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Convex Analysis (Princeton Landmarks in Mathematics and Physics)
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Top Customer Reviews
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).Read more ›
Anyway, if you need a result on convex functions or convex analysis it is very likely that you will find it in ths book.
Most Recent Customer Reviews
I bought the old version. I'm sure the new version is a little easier to read, maybe with some pictures included. Read morePublished on August 8, 2011 by R. Hildebrand
cover almost all aspect; it's easy to understand because things are discussed in R^n (rather than hilbert space, which is also a con of this book)Published on March 8, 2009 by YL
convex programming is a beautiful topic which admits amazing geometric interpretation.
books like this manage to destroy one's appreciation of the topic by not providing... Read more