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On Characterizations of Submanifolds via Smoothness of the Distance Function in Hilbert Spaces

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Abstract

The property of continuous differentiability with Lipschitz derivative of the square distance function is known to be a characterization of prox-regular sets. We show in this paper that the property of higher-order continuous differentiability with locally uniformly continuous last derivative of the square distance function near a point of a set characterizes, in Hilbert spaces, that the set is a submanifold with the same differentiability property near the point.

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Authors and Affiliations

  1. Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

    David Salas

  2. CNRS, Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, Montpellier, France

    Lionel Thibault

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  1. David Salas
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  2. Lionel Thibault
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Correspondence to Lionel Thibault.

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Salas, D., Thibault, L. On Characterizations of Submanifolds via Smoothness of the Distance Function in Hilbert Spaces. J Optim Theory Appl 182, 189–210 (2019). https://doi.org/10.1007/s10957-019-01473-3

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  • DOI: https://doi.org/10.1007/s10957-019-01473-3

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