Unique representation in convex sets by extraction of marked components |
| |
Authors: | D Hinrichsen U Krause |
| |
Institution: | Forschungsschwerpunkt Dynamische Systeme Universität Bremen Bibliothekstraβe Postfach 330 440 2800 Bremen 33, West Germany |
| |
Abstract: | After introducing the basic concepts of extraction and marking for convex sets, the following marked representation theorem is established: Let C be a lineally closed convex set without lines, the face lattice of which satisfies some descending chain condition, and let μ be some marking on C. Then every point of C can be represented in unique way as a convex (nonnegative) linear combination of points (directions) of C which are μ-independent, and this representation can be determined by an algorithm of successive extractions. In particular, if C is a finite dimensional closed convex set without lines and μ marks extreme points (directions) only, then the marked representation theorem contains some well-known results of convex analysis as special cases, and it yields in the case where C is a polyhedral triangulation which extends available results on polytopes to the unbounded case. The triangulation of unbounded polyhedra then is applied to a certain class of parametric linear programs. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|