Efficiency Conditions for Nonsmooth Vector Equilibrium Problems with Constraints via Generalized Subdifferentials

doi:10.1007/s40305-024-00556-x

Abstract

Abstract: This paper is devoted to the study of optimality to a nonsmooth vector equilibrium problem with set, cone and equality constraints. Using a new approach for the Karush-Kuhn-Tucker-type efficiency condition to such problem, we introduce the constraint qualification of the (CQ1) and (CQ2) types via Clarke’s subdifferentials and Michel-Penot’s subdifferentials. We next provide, by using these subdifferentials, some Karush-Kuhn-Tucker (KKT for short) type necessary optimality conditions for efficiency to such problem. Under suitable assumptions on the generalized quasiconvexity/the ?-convexity, some KKT-type necessary optimality conditions become sufficient optimality conditions. Additionally, we provide some KKT-type necessary and sufficient optimality conditions for an efficient solution which does not require that the ordering cone in the objective space has a nonempty interior to those problems. Some illustrative examples are also proposed for our findings.

Key words: Constrained nonsmooth vector equilibrium problem, Efficient solutions, KKT-type efficiency conditions, Constraint qualifications, Generalized subdifferentials

CLC Number:

Tran Van Su, Tran Mau Vinh. Efficiency Conditions for Nonsmooth Vector Equilibrium Problems with Constraints via Generalized Subdifferentials[J]. Journal of the Operations Research Society of China, 2026, 14(1): 80-103.

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