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

Author

Listed:
  • David Salas

    (Universidad de O’Higgins)

  • Lionel Thibault

    (Université de Montpellier)

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.

Suggested Citation

  • David Salas & Lionel Thibault, 2019. "On Characterizations of Submanifolds via Smoothness of the Distance Function in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 189-210, July.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:1:d:10.1007_s10957-019-01473-3
    DOI: 10.1007/s10957-019-01473-3
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    References listed on IDEAS

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    1. Adrian S. Lewis & Jérôme Malick, 2008. "Alternating Projections on Manifolds," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 216-234, February.
    2. CORNET, Bernard, 1983. "Existence of slow solutions for a class of differential inclusions," LIDAM Reprints CORE 539, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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