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 non-negative 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 non-negative orthant is replaced by a convex closed cone K in X, and the usual non-negative 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 K-copositive 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