Talk:Convex analysis

Mathematics Stub‑class High‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Stub	This article has been rated as Stub-class on Wikipedia's content assessment scale.
High	This article has been rated as High-priority on the project's priority scale.

Is there a difference between convex analysis and convex geometry? Perhaps the two should be merged. ??? --Kompik 10:51, 5 October 2007 (UTC)[reply]

expand?

I think this page should probably be expanded from its current 1 sentence description of convex analysis. Perhaps definition of a convex function/set should be given, as well as some basic properties and applications should be given (and mentions of main articles, for instance brief discussion of convex minimization). I would propose a structure like:

Intro/Definitions (Convex set/function)
Separating/Supporting hyperplane
Conjugate/Biconjugate
Convex Optimization

This is just off the top of my head. Does any one else have thoughts on the topic? Zfeinst (talk) 18:17, 23 February 2012 (UTC)[reply]

Your suggestion is good. An extension might also be informed by the spirit of "the bible" of convex analysis, Rockafellar's book, which presents convex analysis as an (oriented) extensions of (real) linear analysis:

affine manifolds generalized to half spaces and other convex sets,
the set containing the derivative generalized to the subdifferential set,
linear operators (and perhaps bilinear operators and bimodules?) generalized and positive linear operators to oriented monotone processes of convex or concave type (unpopular with the hoi polloi but justly praised by the leaders---Robinson, Aubin, several authors from the Romanian school, Borwein) to bifunctions (but this was where the spirit was willing but the mind was weak, for me).

There have been attempts, e.g. by Hörmander and other Swedes, etc., to develop complex convex analysis.

Cheers, Kiefer.Wolfowitz 19:39, 23 February 2012 (UTC)[reply]