A Non-Convex Analogue to Fenchel Duality

Mohammed Bachir (1)

1 Equations d'evolution

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 $0<α \leq 1$).

Domaines: Analyse fonctionnelle [math.FA]

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