Abstract
ABSTRACT In this paper, we first introduce a Hausdorff-type distance by means of a nonlinear scalarization function related to the weighted set order relations, and examine some of its properties. We then use it to define directional derivative for set-valued maps, and derive some of its properties similar to the scalar case. As applications, we obtain necessary and sufficient optimality conditions for set optimization problems. Several examples are given to illustrate our results and the concepts introduced in this paper.
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