Quantitative results on Fejer monotone sequences
Abstract
We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fejer monotonicity where the convergence uses the compactness of the underlying set. These quantitative versions are in the form of explicit rates of so-called metastability in the sense of T. Tao. Our approach covers examples ranging from the proximal point algorithm for maximal monotone operators to various fixed point iterations (x_n) for firmly nonexpansive, asymptotically nonexpansive, strictly pseudo-contractive and other types of mappings. Many of the results hold in a general metric setting with some convexity structure added (so-called W-hyperbolic spaces). Sometimes uniform convexity is assumed still covering the important class of CAT(0)-spaces due to Gromov.
Cite
@article{arxiv.1412.5563,
title = {Quantitative results on Fejer monotone sequences},
author = {Ulrick Kohlenbach and Laurentiu Leustean and Adriana Nicolae},
journal= {arXiv preprint arXiv:1412.5563},
year = {2015}
}