Fixed points of compositions of nonexpansive mappings: finitely many linear reflectors
Functional Analysis
2020-04-28 v1 Optimization and Control
Abstract
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently "nice", then the fixed point set of the composition coincides with the intersection of the individual fixed point sets. In this paper, we explore the situation for compositions of linear reflectors. We provide positive results, upper bounds, and limiting examples. We also discuss classical reflectors in the Euclidean plane.
Cite
@article{arxiv.2004.12582,
title = {Fixed points of compositions of nonexpansive mappings: finitely many linear reflectors},
author = {Salihah Alwadani and Heinz H. Bauschke and Xianfu Wang},
journal= {arXiv preprint arXiv:2004.12582},
year = {2020}
}