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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 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)].

49J52Nonsmooth analysis (other weak concepts of optimality)
58C20Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
90C30Nonlinear programming
58C06Set-valued and function-space valued mappings on manifolds