Vector complementarity and minimal element problems

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Abstract

In this paper, vector complementarity problems are introduced as weak versions of vector variational inequalities in ordered Banach spaces. New dual cones are introduced and proved to be closed. In the sense of efficient point, we prove that the minimal element problem is solvable if a vector variational inequality is solvable; we also prove that any solution of a strong vector variational inequality or positive vector complementarity problem is a solution of the minimal element problem.
Original languageEnglish
Pages (from-to)483-495
Number of pages13
JournalJournal of Optimization Theory and Applications
Volume77
Issue number3
DOIs
Publication statusPublished - 1 Jun 1993
Externally publishedYes

Keywords

  • dual cones
  • minimal element problems
  • Vector complementarity problems
  • vector variational inequalities

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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