A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems

A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems

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In this paper, we introduce Spring the notion of higher-order weak adjacent epiderivative for a set-valued map without lower-order approximating directions and obtain existence theorem and some properties of the epiderivative.Then by virtue of the epiderivative and Benson proper efficiency, we establish the higher-order Mond-Weir type dual problem for a set-valued optimization problem and obtain the corresponding weak duality, strong duality and 6 Piece Power Reclining Sectional converse duality theorems, respectively.