ON OPTIMALITY CONDITIONS FOR EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS WITH CONSTRAINTS VIA CLARKE AND MICHEL-PENOT SUBDIFFERENTIALS

On optimality conditions for efficient solutions of vector equilibrium problem with constraints via Clarke and Michel-Penot subdifferentials
Tác giả: TS. Cộng Sự 1
Nơi đăng: , Số: , Trang: 15 pages, Năm: 2018, Loại bài viết: Bài báo, Quốc gia: Châu Âu.

Abstract:

The main purpose of this article is to study necessary and sufficient optimality conditions for efficient solutions of vector equilibrium problem with conditions defined by set, cone and equality constraints via the Clarke and Michel-Penot subdifferentials. First, under suitable assumptions, necessary optimality conditions for weakly efficient, Henig efficient, globally efficient and superefficient solutions to the vector equilibrium problem with constraints are established. Second, using the generalized quasiconvexity of an objective function together with the $\partial-$ convexity of real-valued functions, sufficient optimality conditions for efficient solutions are obtained. Final, necessary and sufficient optimality conditions for an efficient solution are derived as well.