Abstract
We study optimality conditions of globally efficient solution for vector equilibrium problems with generalized convexity. The necessary and sufficient conditions of globally efficient solution for the vector equilibrium problems are obtained. The Kuhn-Tucker condition of globally efficient solution for vector equilibrium problems is derived. Meanwhile, we obtain the optimality conditions for vector optimization problems and vector variational inequality problems with constraints.
Highlights
Throughout the paper, let X, Y, and Z be real Hausdorff topological vector spaces, D ⊂ X a nonempty subset, and 0Y denotes the zero element of Y
We study the optimality conditions for the vector equilibrium problems
2.4 ii f is said to be C-subconvexlike see 21, if there exists θ ∈ int C such that for all x1, x2 ∈ D, for all λ ∈ 0, 1, for all ε > 0, there exists x3 ∈ D such that εθ f x1 1 − λ f x2 − f x3 ∈ C
Summary
Throughout the paper, let X, Y, and Z be real Hausdorff topological vector spaces, D ⊂ X a nonempty subset, and 0Y denotes the zero element of Y. Consider the vector equilibrium problems with constraints for short, VEPC : finding x ∈ A such that. Giannessi et al turned the vector variational inequalities with constraints into another vector variational inequalities without constraints They gave sufficient conditions for efficient solution and weakly efficient solution of the vector variational inequalities in finite dimensional spaces. Gong presented the necessary and sufficient conditions for weakly efficient solution, Henig efficient solution, and superefficient solution for the vector equilibrium problems with constraints under the condition of cone-convexity. It is important to give the optimality conditions for the solution of VEPC under conditions of generalized convexity. We study the optimality conditions for the vector equilibrium problems. We present the necessary and sufficient conditions for globally efficient solution of VEPC under generalized cone-subconvexlikeness.
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