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A Non-Convex Analogue to Fenchel Duality

Mohammed Bachir 1
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 $0<α \leq 1$).
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Submitted on : Friday, August 7, 2015 - 12:19:04 AM
Last modification on : Tuesday, January 19, 2021 - 11:08:54 AM


  • HAL Id : hal-01183279, version 1



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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