On compositions of special cases of Lipschitz continuous operators
Optimization and Control
2020-01-01 v1
Abstract
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas--Rachford and forward-backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions.
Keywords
Cite
@article{arxiv.1912.13165,
title = {On compositions of special cases of Lipschitz continuous operators},
author = {Pontus Giselsson and Walaa M. Moursi},
journal= {arXiv preprint arXiv:1912.13165},
year = {2020}
}