On the order of the operators in the Douglas-Rachford algorithm
Optimization and Control
2015-05-13 v1 Numerical Analysis
Abstract
The Douglas-Rachford algorithm is a popular method for finding zeros of sums of monotone operators. By its definition, the Douglas-Rachford operator is not symmetric with respect to the order of the two operators. In this paper we provide a systematic study of the two possible Douglas-Rachford operators. We show that the reflectors of the underlying operators act as bijections between the fixed points sets of the two Douglas-Rachford operators. Some elegant formulae arise under additional assumptions. Various examples illustrate our results.
Keywords
Cite
@article{arxiv.1505.02796,
title = {On the order of the operators in the Douglas-Rachford algorithm},
author = {Heinz H. Bauschke and Walaa M. Moursi},
journal= {arXiv preprint arXiv:1505.02796},
year = {2015}
}
Comments
10 pages