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Received October 10, 2019; Accepted June 25, 2020; Published July 2, 2020
Abstract. In this paper, we study the higher-order necessary and sufficient optimality conditions for efficient solutions of vector equilibrium problems with constraints in terms of Studniarski’s derivatives in real Banach spaces. We first propose the constraint qualification of the (CQm) type and then obtain the higher-order Kuhn-Tucker necessary optimality conditions for the efficient solutions, which are not required here that the ordering cone has a non-empty interior. Under suitable assumptions, the higher-order necessary optimality conditions become the higher-order sufficient optimality conditions. Second, under suitable assumptions on the nearly cone-subconvexlikeness, the higher-order Kuhn-Tucker type optimality conditions for efficient solutions in the sense of ordering cones with its interiors nonempty are derived. As applications, some the higher-order Kuhn-Tucker optimality conditions for efficient solutions of constrained vector optimization problem are also established as well. We finally provide several examples to illustrate our results.
How to Cite this Article:
Dinh Dieu Hang, Tran Van Su, On optimality conditions for efficient solutions in constrained vector equilibrium problems in terms of Studniarski’s derivatives, Journal of Nonlinear Functional Analysis, Vol. 2020 (2020), Article ID 27, pp. 1-19 .