Characterizing nonemptiness and compactness of the solution set of a convex vector optimization problem with cone constraints and applications

X. X. Huang, Xiaoqi Yang, K. L. Teo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)

Abstract

In this paper, we characterize the nonemptiness and compactness of the set of weakly efficient solutions of a convex vector optimization problem with cone constraints in terms of the level-boundedness of the component functions of the objective on the perturbed sets of the original constraint set. This characterization is then applied to carry out the asymptotic analysis of a class of penalization methods. More specifically, under the assumption of nonemptiness and compactness of the weakly efficient solution set, we prove the existence of a path of weakly efficient solutions to the penalty problem and its convergence to a weakly efficient solution of the original problem. Furthermore, for any efficient point of the original problem, there exists a path of efficient solutions to the penalty problem whose function values (with respect to the objective function of the original problem) converge to this efficient point.
Original languageEnglish
Pages (from-to)391-407
Number of pages17
JournalJournal of Optimization Theory and Applications
Volume123
Issue number2
DOIs
Publication statusPublished - 1 Nov 2004

Keywords

  • efficient solutions
  • Optimization problem with cone constraints
  • penalization methods
  • weakly efficient solutions

ASJC Scopus subject areas

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

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