Customer Reviews

Convex Analysis (Princeton Landmarks in Mathematics and Physics)

5 star:		(3)
4 star:		(2)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

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.

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.

I bought the old version. I'm sure the new version is a little easier to read, maybe with some pictures included. The old version is very dense, but this can be good if you already know a bit about the field.

This book perhaps ranks with Halmos' "Finite Dimensional Vector Spaces" as an unusually clear description of its subject. Rockafellar's book has been through numerous printings in 40 years. The theorem proofs can be intricate. But the thread of logical development makes reading it worthwhile. Certainly, it is beautiful how the crucial assumption of convexity makes all the derivations possible.

The level of discussion is suitable for a 3rd year undergrad [or higher], who is majoring in maths.

By current standards of maths texts, it does lack diagrams. In fact, there doesn't seem to be a single one! Something to get used to, if you are a current undergrad weaned on recent texts. [Since the author is still alive, perhaps he might consider adding diagrams to a future edition.]

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)

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 even one (gasp!) figure. damn Bourbaki style.

This is a good book for the first year in PhD studies. I recommend amply this book, it's very clear in the explanation, if you have any doubts about topology, Rockafellar explained in this book very simple the theory and all you need about Topology.