# A Non-Convex Analogue to Fenchel Duality

1 Equations d'evolution
SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
Abstract : We introduce and study a new notion of conjugacy, similar to Fenchel conjugacy, in a non-convex setting. Dual versions of Šmulyan's classical result are established in the framework of this conjugacy, which reveal a relation between well-posed problems and the differentiability. As an application we deduce the generic Fréchet differentiability of the norm $‖·‖∞$ in certain spaces of bounded continuous functions (i.e., $Lipα(X)$ for $0<α \leq 1$).
Type de document :
Article dans une revue
Journal of Functional Analysis, Elsevier, 2001, 181 (2), pp.300-312

https://hal-paris1.archives-ouvertes.fr/hal-01183279
Contributeur : Mohammed Bachir <>
Soumis le : vendredi 7 août 2015 - 00:19:04
Dernière modification le : lundi 27 novembre 2017 - 14:14:02

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• HAL Id : hal-01183279, version 1

### Citation

Mohammed Bachir. A Non-Convex Analogue to Fenchel Duality. Journal of Functional Analysis, Elsevier, 2001, 181 (2), pp.300-312. 〈hal-01183279〉

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