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The Fermat Rule for Set Optimization Problems with Lipschitzian Set-Valued Mappings

Gemayqzel Bouza (gema***at***matcom.uh.cu)
Ernest Quintana (ernest.quintana***at***mathematik.uni-halle.de)
Vu Anh Tuan (anh.vu***at***mathematik.uni-halle.de)
Christiane Tammer (christiane.tammer***at***mathematik.uni-halle.de)

Abstract: n this paper, we consider set optimization problems with respect to the set approach. Specifically, we deal with the lower less and the upper less set relations. First, we derive properties of convexity and Lipschitzianity of suitable scalarizing functionals, under the same assumption on the set-valued objective mapping. We then obtain upper estimates of the limiting subdifferential of these functionals. These results, together with the scalarization properties of the functionals, allow us to obtain a Fermat rule for set optimization problems with Lipschitzian data.

Keywords: set valued map, optimality conditions, scalarization, coderivative, subdifferential

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Other Topics (Multi-Criteria Optimization )

Category 3: Robust Optimization


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Entry Submitted: 12/20/2019
Entry Accepted: 12/20/2019
Entry Last Modified: 02/21/2020

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