Talk:Convex analysis

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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.

Good editor Isheden can warn you that I am a fundamentalist about insisting on convex "minimization" unless stationary-points/saddlepoints or convex maximization be also considered.

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