Self-contracted curves are gradient flows of convex functions

Antoine Lemenant; Estibalitz Durand Cartagena

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arXiv · 1802.07542

Self-contracted curves are gradient flows of convex functions

Antoine Lemenant·Estibalitz Durand Cartagena

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Abstract

In this paper we prove that any $C^{1,\alpha}$ curve in $\mathbb{R}^n$, with $\alpha \in (\frac{1}{2},1]$, is the solution of the gradient flow equation for some $C^1$ convex function $f$, if and only if it is strongly self-contracted.

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Antoine Lemenant, Estibalitz Durand Cartagena. 2018-02-21. Self-contracted curves are gradient flows of convex functions. https://arxiv.org/abs/1802.07542

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