Self-contracted curves are gradient flows of convex functions
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- by Estibalitz Durand-Cartagena and Antoine Lemenant PDF
- Proc. Amer. Math. Soc. 147 (2019), 2517-2531 Request permission
Abstract:
In this paper we prove that any $C^{1,\frac {1}{2}}$ curve in $\mathbb {R}^n$ is the solution of the gradient flow equation for some $C^1$ convex function $f$ if and only if it is strongly self-contracted.References
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Additional Information
- Estibalitz Durand-Cartagena
- Affiliation: Departamento de Matemática Aplicada, UNED. ETSI Industriales, Juan del Rosal 12, 28040 Madrid, Spain
- MR Author ID: 869504
- Email: edurand@ind.uned.es
- Antoine Lemenant
- Affiliation: Université Paris 7 (Denis Diderot), Laboratoire Jacques Louis Lions (CNRS UMR 7598), Université Paris Diderot - Paris 7, U.F.R. de Mathématiques, Bâtiment Sophie Germain, 75205 Paris Cedex 13, France
- MR Author ID: 889777
- Email: lemenant@ljll.univ-paris-diderot.fr
- Received by editor(s): February 21, 2018
- Received by editor(s) in revised form: February 22, 2018, July 16, 2018, and August 27, 2018
- Published electronically: February 14, 2019
- Additional Notes: The first author was supported by the grant MTM2015-65825-P (MINECO of Spain).
The second author was supported by the research PGMO grant COCA from the Hadamard Foundation. - Communicated by: Svitlana Mayboroda
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 2517-2531
- MSC (2010): Primary 34A99; Secondary 46N10
- DOI: https://doi.org/10.1090/proc/14407
- MathSciNet review: 3951429