Further study on the LevitinPolyak well-posedness of constrained convex vector optimization problems

X. X. Huang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)

Abstract

In this paper, we first establish characterizations of the nonemptiness and compactness of the set of weakly efficient solutions of a convex vector optimization problem with a general ordering cone (with or without a cone constraint) defined in a finite dimensional space. Using one of the characterizations, we further establish for a convex vector optimization problem with a general ordering cone and a cone constraint defined in a finite dimensional space the equivalence between the nonemptiness and compactness of its weakly efficient solution set and the generalized type I LevitinPolyak well-posednesses. Finally, for a cone-constrained convex vector optimization problem defined in a Banach space, we derive sufficient conditions for guaranteeing the generalized type I LevitinPolyak well-posedness of the problem.
Original languageEnglish
Pages (from-to)1341-1347
Number of pages7
JournalNonlinear Analysis, Theory, Methods and Applications
Volume75
Issue number3
DOIs
Publication statusPublished - 1 Feb 2012

Keywords

  • Cone-constrained optimization
  • Convex vector optimization
  • Ekeland's variational principle
  • Weakly efficient solution set
  • Well-posedness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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