Proximal Smoothness and the Lower{c 2 Property

Abstract

A subset X of a real Hilbert space H is said to be proximally smooth provided that the function d X : H ! R (the distance to X) is continuously diierentiable on an open tube U around X. It is proven that this property is equivalent to d X having a nonempty proximal subgradient at every point of U, and that the (G^ ateaux = Fr echet) derivative is locally… (More)

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