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arXiv · 2205.03156

Discrete-time gradient flows in Gromov hyperbolic spaces

Shin-ichi Ohta
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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.

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Shin-ichi Ohta. 2022-05-06. Discrete-time gradient flows in Gromov hyperbolic spaces. https://arxiv.org/abs/2205.03156

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