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Remarks on second order generalized derivatives for differentiable functions with Lipschitzian Jacobian. (English) Zbl 1057.49016

Given an open subset \(\Omega\) of \(\mathbb{R}^{n}\), a function \(f:\Omega \rightarrow\mathbb{R}\) is called \(C^{1,1}\) if its first-order partial derivatives exist and are locally Lipschitz. For such functions, many of the (generalized) second-order derivatives that have been defined (those of Peano, Riemann, Yang-Jeyakumar, and Hiriart-Urruty among others) are finite. The paper establishes some inequalities between these second-order derivatives and compares optimality conditions associated to them.

MSC:

49J52 Nonsmooth analysis
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26A16 Lipschitz (Hölder) classes
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