Epidifferentiability of the map of infima in Hilbert spaces |
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Authors: | Luis Rodríguez-Marín |
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Institution: | Departamento de Matemática Aplicada, E.T.S.I.I. Universidad Nacional de Educación a Distancia, Calle Juan del Rosal 12, 28040 Madrid, Spain |
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Abstract: | This article deals with derivatives for set-valued maps that take values in ordered vector spaces, in particular it concerns about the relationship between the epiderivatives of a set-valued map and its associated map of infima. When the image space is a real separable Hilbert space ordered by an orthonormal basis, by using a variational technique based on a decoupling of the ordering cone into half-spaces, we show that both epiderivatives coincide under certain hypothesis of compactness and stability. Furthermore we obtain some computation formulas for these derivatives in terms of associated scalar set-valued maps. |
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Keywords: | Ordered Hilbert spaces Set-valued analysis Contingent epiderivatives w r t half-spaces Variational characterization of the infimum Contingent derivatives |
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