Pairs of compact convex sets naturally arise in quasidifferential calculus as sub- and superdifferentials of a quasidifferentiable function (see Dem86). Since the sub- and superdifferentials are not uniquely determined, minimal representations are of special importance. In this paper we give a survey on some recent results on minimal pairs of closed bounded convex sets in a topological vector space (see PALURB). Particular attention is paid to the problem of characterizing minimal representatives of a pair of nonempty compact convex subsets of a locally convex topological vector space in the sense of the Rådström-Hörmander theory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-13,
author = {Diethard Pallaschke and Ryszard Urba\'nski},
title = {Minimal pairs of compact convex sets},
journal = {Banach Center Publications},
volume = {65},
year = {2004},
pages = {147-158},
zbl = {1092.46501},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-13}
}
Diethard Pallaschke; Ryszard Urbański. Minimal pairs of compact convex sets. Banach Center Publications, Tome 65 (2004) pp. 147-158. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-13/