Variational characterization of the contingent epiderivative |
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Authors: | Luis Rodríguez-Marín |
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Institution: | Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal, 12, 28040 Madrid, Spain |
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Abstract: | In this paper the existence of the contingent epiderivative of a set-valued map is studied from a variational perspective. We give a variational characterization of the ideal minimal of a weakly compact set. As a consequence we characterize the existence of the contingent epiderivative in terms of an associated family of variational systems. When a set-valued map takes values in Rn we show that these systems can be formulated in terms of the contingent epiderivatives of scalar set-valued maps. By applying these results we extend some existing theorems. |
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Keywords: | Ordered space Set-valued maps Contingent epiderivative Variational characterization |
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