Convergence analysis of a class of penalty methods for vector optimization problems with cone constraints

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

Abstract

In this paper, we consider convergence properties of a class of penalization methods for a general vector optimization problem with cone constraints in infinite dimensional spaces. Under certain assumptions, we show that any efficient point of the cone constrained vector optimization problem can be approached by a sequence of efficient points of the penalty problems. We also show, on the other hand, that any limit point of a sequence of approximate efficient solutions to the penalty problems is a weekly efficient solution of the original cone constrained vector optimization problem. Finally, when the constrained space is of finite dimension, we show that any limit point of a sequence of stationary points of the penalty problems is a KKT stationary point of the original cone constrained vector optimization problem if Mangasarian-Fromovitz constraint qualification holds at the limit point. 2006.
Original languageEnglish
Pages (from-to)637-652
Number of pages16
JournalJournal of Global Optimization
Volume36
Issue number4
DOIs
Publication statusPublished - 1 Dec 2006

Keywords

  • Convergence
  • Efficiency
  • Level-compactness
  • Penalty method
  • Vector optimization with cone constraints

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research
  • Global and Planetary Change

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