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Global inversion of nonsmooth mappings using pseudo-Jacobian matrices

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Jaramillo Aguado, Jesús Ángel and Madiedo, Oscar and Sánchez González, Luis (2014) Global inversion of nonsmooth mappings using pseudo-Jacobian matrices. Nonlinear Analysis: Theory, Methods & Applications, 108 . pp. 57-65. ISSN 0362-546X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0362546X14001813#




Abstract

We study the global inversion of a continuous nonsmooth mapping f : R-n -> R-n, which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to f, introduced by Jeyakumar and Luc, and we consider a related index of regularity for f. We obtain a characterization of global inversion in terms of its index of regularity. Furthermore, we prove that the Hadamard integral condition has a natural counterpart in this setting, providing a sufficient condition for global invertibility.


Item Type:Article
Uncontrolled Keywords:Global inversion; Pseudo-Jacobian matrices
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:26873
Deposited On:30 Sep 2014 10:58
Last Modified:30 Sep 2014 10:58

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