自收缩曲线是凸函数的梯度流
Self-contracted curves are gradient flows of convex functions
摘要：
本文证明了$\mathbb{R}^n$中的任意$C^{1,α}$曲线，若满足$α\in (\frac{1}{2},1]$，则是某个$C^1$凸函数$f$的梯度流方程的解，当且仅当它是强自收缩的.
英文摘要：
In this paper we prove that any $C^{1,α}$ curve in $\mathbb{R}^n$, with $α\in (\frac{1}{2},1]$, is the solution of the gradient flow equation for some $C^1$ convex function $f$, if and only if it is strongly self-contracted.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
