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A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions

Borwein, Jonathan M. and Preiss, D. (1987) A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions. Trans. Amer. Math. Soc., 303 . pp. 517-527.

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Abstract

We show that, typically, lower semicontinuous functions on a Banach space densely inherit lower subderivatives of the same degree of smoothness as the norm. In particular every continuous convex function on a space with a Gâteaux (weak Hadamard, Fréchet) smooth renorm is densely Gâteaux (weak Hadamard, Fréchet) differentiable. Our technique relies on a more powerful analogue of Ekeland's variational principle in which the function is perturbed by a quadratic-like function. This "smooth" variational principle has very broad applicability in problems of nonsmooth analysis.

Item Type: Article
Subjects: UNSPECIFIED
Faculty: UNSPECIFIED
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 20 Feb 2015 16:20
Last Modified: 20 Feb 2015 16:20
URI: https://docserver.carma.newcastle.edu.au/id/eprint/1597

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