Vectorial penalization for generalized functional constrained problems
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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.
KeywordsSet-valued vector optimization Penalization Bouligand derivative of set-valued maps Necessary optimality conditions
Mathematics Subject Classification49J53 49K27 90C46
This research was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-RU-TE-2014-4-0019.
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