Abstract
This paper is to deal with Mond-Weir duality and Wolfe duality for constrained set-valued optimization problems in terms of cone-directed Clarke derivatives. Firstly, necessary and sufficient optimality conditions for constrained set-valued optimizations in terms of cone-directed Clarke derivatives for the cone-semilocally convex like maps are investigated. Then, the Mond-Weir duality and Wolfe duality for a constrained set-valued optimization and their weak duality, strong duality and converse duality are considered.
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