TY  - GEN
AB  - We consider a class of comprehensive compact  convex polyhedra called _Cephoids_.
A Cephoid is a Minkowski sum of  finitely many standardized simplices ("deGua Simplices'').
The  Pareto surface of Cephoids consists of certain translates of simplices, algebraic sums of subsimplices etc.  The peculiar shape of such a Pareto surface raises the question as to how far results for Cephoids can be carried over to general comprehensive compact  convex bodies by approximation.<br /><br />

We prove that to any comprehensive compact convex body &Gamma; , given a set of finitely many points on its surface, there is a Cephoid &Pi;   that coincides with &Gamma;  in exactly these preset points. As a consequence, Cephoids are dense within the set of comprehensive compact convex bodies with respect to the Hausdorff metric.<br /><br />

  Cephoids  appear in  Operations  Research (Optimization |10|, |3|),   in  Mathematical Economics (Free Trade theory |7|, |8|), and in Cooperative Game Theory (the Maschler--Perles solution |6|).<br /><br />

More generally in the context of Cooperative Game Theory, the notion of a Cephoid serves to construct  "solutions'' or "values'' for  bargaining problems and non--side payment games (|9|).<br /><br />

Therefore, the results of this paper open up an avenue for the extension of solution concepts from Cephoids to  general compact convex bodies.
DA  - 2020
LA  - eng
PY  - 2020
SN  - 0931-6558
SP  - 28-
TI  - Approximating Convex Bodies by Cephoids
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29465297
Y2  - 2024-11-24T04:49:48
ER  -