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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 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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