Geodesic
Self-Dual Smoothing of Convex and Saddle Functions
Journal of convex analysis, Tome 15 (2008) no. 1, pp. 179-19.

Voir la notice de l'article provenant de la source Heldermann Verlag

It is shown that any convex function can be approximated by a family of differentiable with Lipschitz continuous gradient and strongly convex approximates in a "self-dual" way: the conjugate of each approximate is the approximate of the conjugate of the original function. The approximation technique extends to saddle functions, and is self-dual with respect to saddle function conjugacy and also partial conjugacy that relates saddle functions to convex functions.
Classification : 52A41, 90C25, 90C59, 90C46, 26B25
Mots-clés : Convex functions, approximation, Moreau envelopes, duality, saddle functions 
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     author = {R. Goebel},
     title = {Self-Dual {Smoothing} of {Convex} and {Saddle} {Functions}},
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     number = {1},
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}
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R. Goebel. Self-Dual Smoothing of Convex and Saddle Functions. Journal of convex analysis, Tome 15 (2008) no. 1, pp. 179-19. http://geodesic.mathdoc.fr/item/JCA_2008_15_1_JCA_2008_15_1_a11/