How averaged is the composition of two linear projections?
Optimization and Control
2023-03-27 v1 Functional Analysis
Abstract
Projection operators are fundamental algorithmic operators in Analysis and Optimization. It is well known that these operators are firmly nonexpansive; however, their composition is generally only averaged and no longer firmly nonexpansive. In this note, we introduce the modulus of averagedness and provide an exact result for the composition of two linear projection operators. As a consequence, we deduce that the Ogura-Yamada bound for the modulus of the composition is sharp.
Cite
@article{arxiv.2303.13738,
title = {How averaged is the composition of two linear projections?},
author = {Heinz H. Bauschke and Theo Bendit and Walaa M. Moursi},
journal= {arXiv preprint arXiv:2303.13738},
year = {2023}
}