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2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.
We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as...
Cet article a pour objectif de traiter de manière unifiée, avec un sous-différentiel abstrait, certaines propriétés de base des sous-différentiels: les règles de somme approchée, les conditions nécessaires d'optimalité, les propriétés de contrôle par la pente forte, les propriétés de reconstitution des sous-différentiels de type Fréchet, la sous-différentiabilité dense des fonctions semi-continues inférieurement (sci), etc. Nous introduisons une nouvelle condition de qualification (portant sur des...
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