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Local differentiability of distance functions. (English) Zbl 0960.49018

Let \(C\) be a closed subset of a Hilbert space, and let \(x\) be a prescribed point in the boundary of \(C\). The authors discuss the continuous differentiability of the distance function \(\text{dist}[.;C]\) outside of \(C\) on some neighborhood of \(x\). This paper is an important complement to a previous work by F. H. Clarke, R. J. Stern and P. R. Wolenski [J. Convex Anal. 2, No. 1-2, 117-144 (1995; Zbl 0881.49008)].
Reviewer: A.Seeger (Avignon)

MSC:

49J52 Nonsmooth analysis
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
90C30 Nonlinear programming
58C06 Set-valued and function-space-valued mappings on manifolds

Citations:

Zbl 0881.49008
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References:

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