
Accession Number : AD0714822
Title : The Generalized Complementarity Problem.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF OPERATIONS RESEARCH HOUSE
Personal Author(s) : Karamardian,S.
Report Date : AUG 1970
Pagination or Media Count : 17
Abstract : For a given map F from (E sub (+), sup n), the nonnegative orthant of E sup n, into E sup n, the complementarity problem is that of finding an x in (E sub (+), sup n) whose image F(x) is also in (E sub (+), sup n), and such that the two vectors are orthogonal. In this paper a general complementarity problem (GCP) is defined, where the setting is a locally convex Hausdorff topological vector space X, the nonnegative orthant is replaced by a convex closed cone K in X, and the usual nonnegative partial ordering is replaced by preordering, induced by the cone K and its polar cone K*. An existence theorem is given for the (GCP). In the finite dimensional case it is shown that if F is strongly Kcopositive then the (GCP) has a solution. This generalizes similar results of Habetler and Price. (Author)
Descriptors : (*MATHEMATICAL PROGRAMMING, PROBLEM SOLVING), CONVEX SETS, VECTOR SPACES, GAME THEORY, GEOMETRY, THEOREMS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE