Fast Krasnoselskii-Mann Method with Overrelaxation and Preconditioners
Optimization and Control
2025-09-30 v2 Numerical Analysis
Numerical Analysis
Abstract
We study accelerated Krasnoselskii-Mann-type methods with preconditioners in both continuous and discrete time. From a continuous-time model, we derive a generalized fast Krasnoselskii-Mann method, providing a new yet simple proof of convergence that leads to unprecedented flexibility in parameter tuning, allowing up to twice larger relaxation parameters. Our analysis unifies inertial and anchoring acceleration mechanisms and offers a broad range of parameter choices, which prove beneficial in practice. Additionally, we extend our analysis to the case where preconditioners are allowed to be degenerate, unifying the treatment of various splitting methods and establishing the weak convergence of shadow sequences.
Cite
@article{arxiv.2411.18574,
title = {Fast Krasnoselskii-Mann Method with Overrelaxation and Preconditioners},
author = {Radu I. Boţ and Enis Chenchene and Jalal M. Fadili},
journal= {arXiv preprint arXiv:2411.18574},
year = {2025}
}