Some kind of Pareto stationarity for multiobjective problems with equilibrium constraints. (3rd June 2019)

• Record Type: Journal Article
• Authors: Zhang, Peng; Zhang, Jin; Lin, Gui-Hua; Yang, Xinmin
• Is Part Of: Optimization. Volume 68:Number 6(2019)
• Page Start: 1245
• Page End: 1260
• Publication Date: 2019-06-03
• Subjects: Multiobjective problem with equilibrium constraints -- Pareto optimality -- strong Pareto Kuhn-Tucker conditions -- generalized Guignard constraint qualification -- S-stationarity; 90C30 -- 90C33 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1591406
• Languages: English
• ISSNs: 0233-1934

Abstract

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.