Discrete-time gradient flows in Gromov hyperbolic spaces
Optimization and Control
2025-02-03 v3 Metric Geometry
Abstract
We investigate fundamental properties of the proximal point algorithm for Lipschitz convex functions on (proper, geodesic) Gromov hyperbolic spaces. We show that the proximal point algorithm from an arbitrary initial point can find a point close to a minimizer of the function. Moreover, we establish contraction estimates (akin to trees) for the proximal (resolvent) operator. Our results can be applied to small perturbations of trees.
Cite
@article{arxiv.2205.03156,
title = {Discrete-time gradient flows in Gromov hyperbolic spaces},
author = {Shin-ichi Ohta},
journal= {arXiv preprint arXiv:2205.03156},
year = {2025}
}
Comments
17 pages; v3: minor modification in Theorem 1.3(i), to appear in Israel J. Math