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Global inversion of nonsmooth mappings using pseudo-Jacobian matrices

Authors :
Jaramillo, Jesús A.
Madiedo, Oscar
Sánchez-González, Luis
Publication Year :
2013

Abstract

We study the global inversion of a continuous nonsmooth mapping $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$, 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.<br />Comment: 12 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1311.2815
Document Type :
Working Paper