Minimal pairs of compact convex sets

Volume 64 / 2004

Diethard Pallaschke, Ryszard Urbański Banach Center Publications 64 (2004), 147-158 MSC: 26A27, 90C30. DOI: 10.4064/bc64-0-13


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.


  • Diethard PallaschkeInstitut für Statistik und Mathematische Wirtschaftstheorie
    Universität Karlsruhe
    Kaiserstr. 12
    D-76128 Karlsruhe, Germany
  • Ryszard UrbańskiWydzia/l Matematyki i Informatyki, Uniwersytet im. Adama
    Mickiewicza Umultowska 87,
    PL-61-614 Poznań, Poland

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