On the Structure of the Weakly Efficient Set for Quasiconvex Vector Minimization

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3 Citations (Scopus)

Abstract

We investigate conditions under which the weakly efficient set for minimization of m objective functions on a closed and convex X⊂ R d (m> d) is fully determined by the weakly efficient sets for all n-objective subsets for some n< m. For quasiconvex functions, it is their union with n= d+ 1. For lower semi-continuous explicitly quasiconvex functions, the weakly efficient set equals the linear enclosure of their union with n= d, as soon as it is bounded. Sufficient conditions for the weakly efficient set to be bounded or unbounded are also investigated.

Original languageEnglish
Pages (from-to)547–564
Number of pages18
JournalJournal of Optimization Theory and Applications
Volume184
Issue number2
DOIs
Publication statusPublished - 7 Dec 2019

Keywords

  • Weakly efficient set
  • Quasiconvex functions
  • Multiobjective
  • Helly’s theorem
  • Linear enclosure

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