English

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}
}