A Hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization
نویسندگان
چکیده
In this paper, we follow Kuroiwa’s set approach in set optimization, which proposes to compare values of a set-valued objective map F respect to various set order relations. We introduce a Hausdorff-type distance relative to an ordering cone between two sets in a Banach space and use it to define a directional derivative for F . We show that the distance has nice properties regarding set order relations and the directional derivative enjoys most properties of the one of a scalarsingle-valued function. These properties allow us to derive necessary and/or sufficient conditions for various types of maximizers and minimizers of F .
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