Behr, Florian and Dolzmann, Georg (2024) A Note on Clarke's Generalized Jacobian for the Inverse of Bi-Lipschitz Maps. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 200. pp. 852-857. ISSN 0022-3239, 1573-2878
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Clarke's inverse function theorem for Lipschitz mappings states that a bi-Lipschitz mapping f is locally invertible about a point x(0) if the generalized Jacobian partial derivative f (x(0)) does not contain singular matrices. It is shown that under these assumptions the generalized Jacobian of the inverse mapping at f (x(0)) is the convex hull of the set of matrices that can be obtained as limits of sequences J(f)(x(k))(-1) with f differentiable in x(k) and x(k) converging to x(0). This identity holds as well if f is assumed to be locally bi-Lipschitz at x(0).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Inverse mapping; Lipschitz continuous mapping; Clarke Jacobian |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Georg Dolzmann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 21 Feb 2024 10:41 |
| Last Modified: | 04 Mar 2025 06:46 |
| URI: | https://pred.uni-regensburg.de/id/eprint/58915 |
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