Random iterations of paracontraction maps and applications to feasibility problems
Dynamical Systems
2020-08-12 v1 Optimization and Control
Abstract
In this paper, we consider the problem of finding an almost surely common fixed point of a family of paracontraction maps indexed on a probability space, which we refer to as the stochastic feasibility problem. We show that a random iteration of paracontraction maps driven by an ergodic stationary sequence converges, with probability one, to a solution of the stochastic feasibility problem, provided a solution exists. As applications, we obtain non-white noise randomized algorithms to solve the stochastic convex feasibility problem and the problem of finding an almost surely common zero of a collection of maximal monotone operators.
Cite
@article{arxiv.2008.04831,
title = {Random iterations of paracontraction maps and applications to feasibility problems},
author = {Edgar Matias and Majela Pentón Machado},
journal= {arXiv preprint arXiv:2008.04831},
year = {2020}
}