Inertial Krasnoselskii-Mann Iterations
Optimization and Control
2023-08-23 v4
Abstract
We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and linear convergence are obtained in the quasi-contractive setting. In both cases, we highlight the relationship with the non-inertial case, and show that passing from one regime to the other is a continuous process in terms of the hypotheses on the parameters. Numerical illustrations are provided for an inertial primal-dual method and an inertial three-operator splitting algorithm, whose performance is superior to that of their non-inertial counterparts.
Cite
@article{arxiv.2210.03791,
title = {Inertial Krasnoselskii-Mann Iterations},
author = {Juan José Maulén and Ignacio Fierro and Juan Peypouquet},
journal= {arXiv preprint arXiv:2210.03791},
year = {2023}
}