Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions
Dynamical Systems
2010-09-14 v1 Optimization and Control
Abstract
We hereby introduce and study the notion of self-contracted curves, which encompasses orbits of gradient systems of convex and quasiconvex functions. Our main result shows that bounded self-contracted planar curves have a finite length. We also give an example of a convex function defined in the plane whose gradient orbits spiral infinitely many times around the unique minimum of the function.
Keywords
Cite
@article{arxiv.0809.0150,
title = {Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions},
author = {Aris Daniilidis and Olivier Ley and Stéphane Sabourau},
journal= {arXiv preprint arXiv:0809.0150},
year = {2010}
}