Linear and strong convergence of algorithms involving averaged nonexpansive operators
Optimization and Control
2014-02-25 v1 Functional Analysis
Numerical Analysis
Abstract
We introduce regularity notions for averaged nonexpansive operators. Combined with regularity notions of their fixed point sets, we obtain linear and strong convergence results for quasicyclic, cyclic, and random iterations. New convergence results on the Borwein-Tam method (BTM) and on the cylically anchored Douglas-Rachford algorithm (CADRA) are also presented. Finally, we provide a numerical comparison of BTM, CADRA and the classical method of cyclic projections for solving convex feasibility problems.
Cite
@article{arxiv.1402.5460,
title = {Linear and strong convergence of algorithms involving averaged nonexpansive operators},
author = {Heinz H. Bauschke and Dominikus Noll and Hung M. Phan},
journal= {arXiv preprint arXiv:1402.5460},
year = {2014}
}
Comments
25 pages