I'm wondering if anyone can give a good reference for a text on convex analysis covering things like support functions, conjugate functions, separation theorems, and aspects of convex analysis in infinite-dimensional spaces (e.g., real topological vector spaces).
I know of three:
- Variational Analysis by Rockafellar
- Convex Analysis by Rockafellar
- Fundamentals of Convex Analysis by Hirart-Urruty and Lemaréchal
I would especially be interested in anyone can give a comparison of these texts (especially between the two Rockafellar texts), and/or any other text suggestions. The audience is students who have had a course or two in analysis (so exposure to basic notions in metric spaces and functional analysis) and people who are particularly interested in theoretical aspects of e.g. mathematical programming, statistics, applied mathematics, though I'm not looking for a text on convex optimization.
Variational analysis by Rockafellar/Wets does a good job of providing geometric illustration and intuition for the subjects you mentioned. It's quite verbose as opposed to "convex analysis" which can be helpful. Also, it provides lots of rigorous proofs. I'm not familiar with the third book you mentioned.
An excellent reference text with a proper treatment of the infinite dimensional setting would be Bauschke and Combettes' book on convex analysis and monotone operator theory. However, it can be a dense read for a beginner. It has lots of more "modern" results with proof, but fewer statements regarding the "intuition" or geometry.