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Subdifferentials of Distance Functions, Approximations and Enlargements

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Abstract

In this work, we study some subdifferentials of the distance function to a nonempty nonconvex closed subset of a general Banach space. We relate them to the normal cone of the enlargements of the set which can be considered as regularizations of the set.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, av. de l’Université BP 1155, 64013, PAU Cédex, France

    Jean-Paul Penot

  2. Business Unit : Bank and Financials, SODIFRANCE, 104 rue Castagnary, 75015, Paris, France

    Robert Ratsimahalo

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  1. Jean-Paul Penot
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  2. Robert Ratsimahalo
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Correspondence to Jean-Paul Penot or Robert Ratsimahalo.

Additional information

The research of this work has been partly carried out when the second author was visiting the Department of Mathematics at the Chinese University of Hong-Kong, at the invitation of Prof. K.F. NG. The visit was made possible by financial supports from the Research Council of Hong-Kong, and from the General Consulate of France

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Penot, JP., Ratsimahalo, R. Subdifferentials of Distance Functions, Approximations and Enlargements. Acta Math Sinica 23, 507–520 (2007). https://doi.org/10.1007/s10114-005-0763-6

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  • DOI: https://doi.org/10.1007/s10114-005-0763-6

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