Discrete-time gradient flows in Gromov hyperbolic spaces
arXiv:2205.03156
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.
17 pages; v3: minor modification in Theorem 1.3(i), to appear in Israel J. Math