The computational content of super strongly nonexpansive mappings and uniformly monotone operators
Optimization and Control
2023-08-14 v3 Functional Analysis
Logic
Abstract
Recently, Liu, Moursi and Vanderwerff have introduced the class of super strongly nonexpansive mappings as a counterpart to operators which are maximally monotone and uniformly monotone. We give a quantitative study of these notions in the style of proof mining, providing a modulus of super strong nonexpansiveness, giving concrete examples of it and connecting it to moduli associated to uniform monotonicity. For the supercoercive case, we analyze the situation further, yielding a quantitative inconsistent feasibility result for this class (obtaining effective uniform rates of asymptotic regularity), a result which is also qualitatively new.
Keywords
Cite
@article{arxiv.2303.02768,
title = {The computational content of super strongly nonexpansive mappings and uniformly monotone operators},
author = {Andrei Sipos},
journal= {arXiv preprint arXiv:2303.02768},
year = {2023}
}