Convergence of Proximal Splitting Algorithms in CAT(k) Spaces and Beyond
Optimization and Control
2021-12-13 v1 Functional Analysis
Abstract
In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric subregularity. Linear metric subregularity is in any case necessary for linearly convergent fixed point sequences, so the result is tight. To show this, we develop a theory of fixed point mappings that violate the usual assumptions of nonexpansiveness and firm nonexpansiveness in p-uniformly convex spaces.
Cite
@article{arxiv.2105.05691,
title = {Convergence of Proximal Splitting Algorithms in CAT(k) Spaces and Beyond},
author = {Florian Lauster and D. Russell Luke},
journal= {arXiv preprint arXiv:2105.05691},
year = {2021}
}
Comments
18 pages, 13 citations. arXiv admin note: text overlap with arXiv:2104.11302