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Moderate second-order derivatives of nondifferentiable functions. (Dérivées secondes modérées de fonctions non dérivables.) (French) Zbl 0789.46034
Summary: Two kinds of second-order generalized derivatives are introduced, with their associated fans. They coincide with the usual second derivative when the later exists. They are more precise than the corresponding notions of Cominetti and Correa but lack their automatic upper semicontinuity properties. These derivatives can be used to characterize convex functions and to formulate optimality conditions.

MSC:
46G05 Derivatives of functions in infinite-dimensional spaces
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
49J52 Nonsmooth analysis
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