A Set-Valued Analysis Approach to Second Order Differentiation of Nonsmooth Functions |
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| Authors: | Miguel Sama |
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| Affiliation: | (1) 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: | A theory of second order differentiability for real functions with calm Clarke gradient at points of strict differentiability is presented from a set-valued analysis perspective by using the theory of graphical derivatives of set-valued maps. Connections with other second order theories and applications in optimization are given. This work is partially supported by Ministerio de Educación y Ciencia (Spain), project MTM2006-02629 and IngenioMathematica (i-MATH) CSD2006-00032 (Consolider-Ingenio 2010). |
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| Keywords: | Nonsmooth analysis Second order differentiation Graphical derivatives of set-valued maps Ordered spaces |
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