Vector optimization problems with nonconvex preferences

N. J. Huang, A. M. Rubinov, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)

Abstract

In this paper, some vector optimization problems are considered where pseudo-ordering relations are determined by nonconvex cones in Banach spaces. We give some characterizations of solution sets for vector complementarity problems and vector variational inequalities. When the nonconvex cone is the union of some convex cones, it is shown that the solution set of these problems is either an intersection or an union of the solution sets of all subproblems corresponding to each of these convex cones depending on whether these problems are defined by the nonconvex cone itself or its complement. Moreover, some relations of vector complementarity problems, vector variational inequalities, and minimal element problems are also given.
Original languageEnglish
Pages (from-to)765-777
Number of pages13
JournalJournal of Global Optimization
Volume40
Issue number4
DOIs
Publication statusPublished - 1 Apr 2008

Keywords

  • Nonconvex cone
  • Vector complementarity problem
  • Vector optimization problem
  • Vector variational inequality

ASJC Scopus subject areas

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

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