Abstract

In this paper we use a double penalization procedure in order to reduce a set-valued optimization problem with functional constraints to an unconstrained one. The penalization results are given in several cases: for weak and strong solutions, in global and local settings, and considering two kinds of epigraphical mappings of the set-valued map that defines the constraints. Then necessary and sufficient conditions are obtained separately in terms of Bouligand derivatives of the objective and constraint mappings.

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