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Differentiability properties of functions that are \(\ell \)-stable at a point. (English) Zbl 1146.49017

Summary: The class of the \(\ell \)-stable functions is introduced in previous papers of the authors as a generalization of the class of \(C^{1,1}\) functions. The importance of this class is that minimization problems with \(\ell \)-stable data admit second-order optimality conditions in terms of suitable directional derivatives similar to those for ones with \(C^{1,1}\) data. The present paper studies differentiability properties of \(\ell \)-stable functions in normed spaces and generalizes to infinite-dimensional spaces some results of the authors.

MSC:

49K10 Optimality conditions for free problems in two or more independent variables
26B05 Continuity and differentiation questions
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