# Linear and strong convergence of algorithms involving averaged nonexpansive operators

arXiv: https://arxiv.org/abs/1402.5460 · HTML: https://mlsanity.com/paper/1402.5460/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2014.

## Built on by (most cited first, 2 of 2)

- [Trilevel and Multilevel Optimization using Monotone Operator Theory](https://mlsanity.com/paper/2105.09407/) (2021)
- [Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees](https://mlsanity.com/paper/2601.07665/) (2026)

## Abstract (arXiv)

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.