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

Title: A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions
Creator: Borwein, J. M.; Preiss , D.
Relation: Transactions of the American Mathematical Society Vol. 303, Issue 2, p. 517-527
Publisher Link: http://dx.doi.org/10.1090/S0002-9947-1987-0902782-7
Publisher: American Mathematical Society
Resource Type: journal article
Date: 1987
Description: 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.
Subject: weak Asplund spaces; subderivatives; renorms; nonsmooth analysis; Ekeland's principle; proximal normals
Identifier: http://hdl.handle.net/1959.13/940776
Identifier: uon:13097
Identifier: ISSN:0002-9947
Rights: First published in Transactions of the American Mathematical Society in Vol. 303, No. 2, pp. 517-527, 1987, published by the American Mathematical Society.
Language: eng
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