Linear convergence of relocated fixed-point iterations
Optimization and Control
2025-12-16 v1
Abstract
We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the algorithmic operator is a contraction. As a key application of our framework, we obtain linear convergence of the relocated Douglas--Rachford algorithm for finding a zero in the sum of two monotone operators in a setting with Lipschitz continuity and strong monotonicity assumptions. We also apply the framework to deduce linear convergence of variable stepsize resolvent splitting algorithms for multioperator monotone inclusions.
Cite
@article{arxiv.2512.12954,
title = {Linear convergence of relocated fixed-point iterations},
author = {Felipe Atenas and Farhana Ahmed Simi and Matthew K Tam},
journal= {arXiv preprint arXiv:2512.12954},
year = {2025}
}