Pairs of Compact Convex Sets
Subtitle: Fractional Arithmetic with Convex Sets
By: by Diethard Pallaschke, Ryszard Urbański
Contributors: Urbański, Ryszard
Series: Mathematics and Its Applications -- 548; Mathematics and Its Applications -- 548
Publisher: Springer Netherlands
Published: 2002
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 295
ISBN-13: 9789048161492; 9789401599207
Subjects: Mathematics; Mathematical optimization; Discrete groups
Description: The book is devoted to the theory of pairs of compact convex sets and in particular to the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the Rådström-Hörmander Theory. Minimal pairs of compact convex sets arise naturally in different fields of mathematics, as for instance in non-smooth analysis, set-valued analysis and in the field of combinatorial convexity. In the first three chapters of the book the basic facts about convexity, mixed volumes and the Rådström-Hörmander lattice are presented. Then, a comprehensive theory on inclusion-minimal representants of pairs of compact convex sets is given. Special attention is given to the two-dimensional case, where the minimal pairs are uniquely determined up to translations. This fact is not true in higher dimensional spaces and leads to a beautiful theory on the mutual interactions between minimality under constraints, separation and decomposition of convex sets, convexificators and invariants of minimal pairs.
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