Some kind of Pareto stationarity for multiobjective problems with equilibrium constraints

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.

KEYWORDS:

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

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 90C30
• 90C33
• 90C46

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by National Natural Science Foundation of China NSFC (Nos. 11671250, 11431004, 71831008, 11601458) and Humanity Social Science Foundation of Ministry of Education of China (No. 15YJA630034). HKBU FRG1/16-17/007, FRG2/16-17/101, RC-NACAN-ZHANG J.