Weak sharp minima for set-valued vector variational inequalities with an application

J. Li, N. J. Huang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)

Abstract

In this paper, the notion of weak sharp minima is employed to the investigation of set-valued vector variational inequalities. The gap function φTfor set-valued strong vector variational inequalities (for short, SVVI) is proved to be less than the gap function φ{symbol}Tfor set-valued weak vector variational inequalities (for short, WVVI) under certain conditions, which implies that the solution set of SVVI is equivalent to the solution set of WVVI. Moreover, it is shown that weak sharp minima for the solution sets of SVVI and WVVI hold for sqrt(min1 ≤ i ≤ npTi) and for gap functions sqrt(φT) and sqrt(φ{symbol}T) under the assumption of strong pseudomonotonicity, where pTiis a gap function for i-th component of SVVI and WVVI. As an application, the weak Pareto solution set of vector optimization problems (for short, VOP) is proved to be weak sharp minimum for sqrt(min1 ≤ i ≤ np∇ gi) when each component giof objective function is strongly convex.
Original languageEnglish
Pages (from-to)262-272
Number of pages11
JournalEuropean Journal of Operational Research
Volume205
Issue number2
DOIs
Publication statusPublished - 1 Sep 2010

Keywords

  • Gap function
  • Set-valued weak (res., strong) vector variational inequality
  • Strong convexity
  • Strong pseudomonotonicity
  • Weak sharp minimum

ASJC Scopus subject areas

  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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