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Generalization of $C^{1,1}$ Property in Infinite Dimension
Marie Dvorská
,
Karel Pastor
Abstract
The class of functions with locally Lipschitz gradient, i.e., the class of $C^{1,1}$ functions, has been deeply studied and many optimization conditions has been stated for this class. A generalization of $C^{1,1}$ property leads to the class of $\ell$–stable functions. In this paper, we study two formally different definitions of $\ell$–stability in infinite dimension and show their equivalence.