Pairs of Compact Convex Sets - Fractional Arithmetic with Convex Sets

Pairs of compact convex sets arise in the quasidifferential calculus of V.F. Demyanov and A.M. Rubinov as sub- and superdifferentials of quasidifferen tiable functions (see [26]) and in the formulas for the numerical evaluation of the Aumann-Integral which were recently introduced in a series of papers by R. Baier and F. Lempio (see [4], [5], [10] and [9]) and R. Baier and E.M. Farkhi [6], [7], [8]. In the field of combinatorial convexity G. Ewald et al. [36] used an interesting construction called virtual polytope, which can also be represented as a pair of polytopes for the calculation of the combinatorial Picard group of a fan. Since in all mentioned cases the pairs of compact con vex sets are not uniquely determined, minimal representations are of special to the existence of minimal pairs of compact importance. A problem related convex sets is the existence of reduced pairs of convex bodies, which has been studied by Chr. Bauer (see [14]).

List of contents

I Convexity.- 1 Convex Sets and Sublinearity.- 2 Topological Vector Spaces.- 3 Compact Convex Sets.- II Minimal Pairs.- 4 Minimal Pairs of Convex Sets.- 5 The Cardinality of Minimal Pairs.- 6 Minimality under Constraints.- 7 Symmetries.- 8 Decompositions.- 9 Invariants.- 10 Applications.- III Semigroups.- 11 Fractions.- 12 Piecewise Linear Functions.- Open Questions.- List of Symbols.

Product details

• Authors: Diethard Pallaschke, Diethard E. 10001477588 Pallaschke, Diethard Erns Pallaschke, Diethard Ernst Pallaschke, R Urbanski, R. Urbanski, Ryszard Urbanski
• Publisher: Springer Netherlands
• Languages: English
• Product format: Paperback / Softback
• Released: 08.10.2010
• EAN: 9789048161492
• ISBN: 978-90-481-6149-2
• No. of pages: 295
• Weight: 476 g
• Illustrations: XII, 295 p.
• Series: Mathematics and Its Applications; Mathematics and its Applications
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; Optimierung, B, Optimization, Diskrete Mathematik, minimum, Interaction, Mathematics and Statistics, Discrete Mathematics, Discrete geometry, Convex and Discrete Geometry, Mathematical optimization, Sets, functions, symmetric relation, semigroup, Prime number, cardinality