Some kind of Pareto stationarity for multiobjective problems with equilibrium constraints

Peng Zhang, Jin Zhang, Gui Hua Lin*, Xinmin Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this paper, we derive some optimality and stationarity conditions for a multiobjective problem with equilibrium constraints (MOPEC). In particular, under a generalized Guignard constraint qualification, we show that any locally Pareto optimal solution of MOPEC must satisfy the strong Pareto Kuhn-Tucker optimality conditions. We also prove that the generalized Guignard constraint qualification is the weakest constraint qualification for the strong Pareto Kuhn-Tucker optimality. Furthermore, under certain convexity or generalized convexity assumptions, we show that the strong Pareto Kuhn-Tucker optimality conditions are also sufficient for several popular locally Pareto-type optimality conditions for MOPEC.

Original languageEnglish
Pages (from-to)1245-1260
Number of pages16
JournalOptimization
Volume68
Issue number6
DOIs
Publication statusPublished - 3 Jun 2019

Scopus Subject Areas

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

User-Defined Keywords

  • generalized Guignard constraint qualification
  • Multiobjective problem with equilibrium constraints
  • Pareto optimality
  • S-stationarity
  • strong Pareto Kuhn-Tucker conditions

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