OPTIMALITY CONDITIONS FOR THE EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS WITH CONSTRAINTS IN TERMS OF DIRECTIONAL DERIVATIVES AND ITS APPLICATIONS

Optimality conditions for the efficient solutions of vector equilibrium problems with constraints in terms of directional derivatives and its applications
Tác giả: TS. Cộng Sự 1
Nơi đăng: , Số: , Trang: 36 pages, Năm: 2018, Loại bài viết: Bài báo, Quốc gia: Châu Âu.

Abstract:

The aim of  this paper is to establish Kuhn-Tucker optimality conditions for constrained vector equilibrium problems in terms of directional derivatives in Banach spaces. Under assumptions on generalized convexity of real-valued functions, Kuhn-Tucker necessary and sufficient optimality conditions for efficient solution, weakly efficient solution, Henig efficient solution, globally efficient solution and superefficient solution of vector equilibrium problems with constraints are established. Some applications to vector variational inequality and vector optimization problems are given. Besides, (strong) Karush-Kuhn-Tucker necessary and sufficient optimality conditions for weakly efficient solutions of the models of transportion-production and Nash-Cournot equilibria problems are obtained. Several examples to illustrate the main results also are derived as well.