Scalar multiplier rules in set-valued optimization

Authors:
Elvira Hernández;Luis Rodríguez-Marín;Miguel Sama
Affiliations:
Departamento de Matemática Aplicada, E.T.S.I.I, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal, 12. 28040 Madrid, Spain;Departamento de Matemática Aplicada, E.T.S.I.I, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal, 12. 28040 Madrid, Spain;Departamento de Matemática Aplicada, E.T.S.I.I, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal, 12. 28040 Madrid, Spain
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this work we establish necessary and sufficient conditions for weak minimizers of a constrained set-valued optimization problem. These conditions are given by means of multiplier rules formulated in terms of contingent epiderivatives of scalar set-valued maps. We consider that the image spaces are finite dimensional and the set-valued maps are convex and stable. For these conditions, our results provide a scalar version of analogous existing results in the literature under weaker existence conditions. Moreover we prove that the multiplier rules can be computed in terms of the directional derivative of associated maps of infima.