The Generalized Complementarity Problem.

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)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1970
Accession Number
AD0714822

Entities

People

  • S. Karamardian

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Operations Research

Technology Areas

  • Space