Given an open subset Ω of ℝn, a function f:Ω→ℝ is called C1,1 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
Remarks on second order generalized derivatives for differentiable functions with Lipschitzian Jacobian / D. La Torre, M. Rocca. - In: APPLIED MATHEMATICS E-NOTES. - ISSN 1607-2510. - 3:(2003), pp. 130-137.
Remarks on second order generalized derivatives for differentiable functions with Lipschitzian Jacobian
D. La TorrePrimo
;
2003
Abstract
Given an open subset Ω of ℝn, a function f:Ω→ℝ is called C1,1 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
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