English

Self-contracted curves are gradient flows of convex functions

Analysis of PDEs 2018-02-22 v1

Abstract

In this paper we prove that any C1,αC^{1,\alpha} curve in Rn\mathbb{R}^n, with α(12,1]\alpha \in (\frac{1}{2},1], is the solution of the gradient flow equation for some C1C^1 convex function ff, if and only if it is strongly self-contracted.

Keywords

Cite

@article{arxiv.1802.07542,
  title  = {Self-contracted curves are gradient flows of convex functions},
  author = {Antoine Lemenant and Estibalitz Durand Cartagena},
  journal= {arXiv preprint arXiv:1802.07542},
  year   = {2018}
}