Affine nonexpansive operators, Attouch-Th\'era duality and the Douglas-Rachford algorithm
Optimization and Control
2016-04-01 v1
Abstract
The Douglas-Rachford splitting algorithm was originally proposed in 1956 to solve a system of linear equations arising from the discretization of a partial differential equation. In 1979, Lions and Mercier brought forward a very powerful extension of this method suitable to solve optimization problems. In this paper, we revisit the original affine setting. We provide a powerful convergence result for finding a zero of the sum of two maximally monotone affine relations. As a by product of our analysis, we obtain results concerning the convergence of iterates of affine nonexpansive mappings as well as Attouch-Th\'era duality. Numerous examples are presented.
Keywords
Cite
@article{arxiv.1603.09418,
title = {Affine nonexpansive operators, Attouch-Th\'era duality and the Douglas-Rachford algorithm},
author = {Heinz H. Bauschke and Brett Lukens and Walaa M. Moursi},
journal= {arXiv preprint arXiv:1603.09418},
year = {2016}
}