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Sequential ε-Subdifferential Calculus for Scalar and Vector Mappings

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Abstract

In this paper, several sequential formulae are obtained for the Brøndsted-Rockafellar ε-subdifferential of the sum and the composition of two convex and lower semicontinuous mappings defined in reflexive Banach spaces. These calculus rules are stated in terms of limits of ε-subgradients at nearby points to the nominal point without assuming any qualification condition, and extend some well-known sequential formulae for the Fenchel subdifferential. Next, as a consequence of these formulae, sequential sum and composition rules for a proper ε-subdifferential of extended vector mappings are obtained, which involve a type of vector strong ε-subdifferential.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S. de Ingenieros de Telecomunicación, Universidad de Valladolid, Paseo de Belén 15, Campus Miguel Delibes, 47011, Valladolid, Spain

    C. Gutiérrez

  2. Departamento de Matemática Aplicada, E.T.S.I. Industriales, UNED, c/ Juan del Rosal 12, Ciudad Universitaria, 28040, Madrid, Spain

    L. Huerga & V. Novo

  3. Institut de Mathématiques et de Modélisation, Université Montpellier, Place Eugène Bataillon, 34095, Montpellier, France

    L. Thibault

Authors
  1. C. Gutiérrez
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  2. L. Huerga
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  3. V. Novo
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  4. L. Thibault
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Corresponding author

Correspondence to V. Novo.

Additional information

This work was partially supported by Ministerio de Economía y Competitividad (Spain) under project MTM2012-30942.

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Gutiérrez, C., Huerga, L., Novo, V. et al. Sequential ε-Subdifferential Calculus for Scalar and Vector Mappings. Set-Valued Var. Anal 25, 383–403 (2017). https://doi.org/10.1007/s11228-016-0386-3

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  • DOI: https://doi.org/10.1007/s11228-016-0386-3

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