On circumcenter mappings induced by nonexpansive operators
Optimization and Control
2018-11-29 v1
Abstract
We introduce the circumcenter mapping induced by a set of (usually nonexpansive) operators. One prominent example of a circumcenter mapping is the celebrated Douglas--Rachford splitting operator. Our study is motivated by the Circumcentered--Douglas--Rachford method recently introduced by Behling, Bello Cruz, and Santos in order to accelerate the Douglas--Rachford method for solving certain classes of feasibility problems. We systematically explore the properness of the circumcenter mapping induced by reflectors or projectors. Numerous examples are presented. We also present a version of Browder's demiclosedness principle for circumcenter mappings.
Cite
@article{arxiv.1811.11420,
title = {On circumcenter mappings induced by nonexpansive operators},
author = {Heinz H. Bauschke and Hui Ouyang and Xianfu Wang},
journal= {arXiv preprint arXiv:1811.11420},
year = {2018}
}
Comments
There are 30 pages and 7 figures