A Non-Convex Analogue to Fenchel Duality
Bachir, Mohammed
HAL, hal-01183279 / Harvested from HAL
Text on HAL
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 $0<α \leq 1$).
Publié le : 2001-07-04
Classification:  [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 
@article{hal-01183279,
     author = {Bachir, Mohammed},
     title = {A Non-Convex Analogue to Fenchel Duality},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01183279}
}

Bachir, Mohammed. A Non-Convex Analogue to Fenchel Duality. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-01183279/