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29 March 2024
 
  » arxiv » 1311.2815

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Global inversion of nonsmooth mappings using pseudo-Jacobian matrices
Jesús A. Jaramillo ; Oscar Madiedo ; Luis Sánchez-González ;
Date 12 Nov 2013
AbstractWe study the global inversion of a continuous nonsmooth mapping $f: mathbb{R}^n ightarrow mathbb{R}^n$, 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.
Source arXiv, 1311.2815
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