# Self-contracted curves are gradient flows of convex functions

created by durandcar on 20 Feb 2018
modified by lemenant on 22 Feb 2018

[BibTeX]

Preprint

Inserted: 20 feb 2018
Last Updated: 22 feb 2018

Year: 2018

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.