Abstract
In this paper, we provide in a general Hilbert space new characterizations of uniform prox-regularity involving outside but sufficiently close points of considered sets. We show that the complement of a prox-regular set is nothing but the union of closed balls with common radius. We derive from this that the prox-regularity of a given closed set is equivalent to the semiconvexity property of its distance function. Various estimates involving the metric projection mapping to a prox-regular set are also established.
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The first author has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No 823731 CONMECH.
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Nacry, F., Thibault, L. Distance Function Associated to a Prox-regular set. Set-Valued Var. Anal 30, 731–750 (2022). https://doi.org/10.1007/s11228-021-00616-x
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DOI: https://doi.org/10.1007/s11228-021-00616-x