# Line Search for Averaged Operator Iteration

arXiv: https://arxiv.org/abs/1603.06772 · HTML: https://mlsanity.com/paper/1603.06772/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2016.

## Built on by (most cited first, 3 of 3)

- [From Noisy Fixed-Point Iterations to Private ADMM for Centralized and Federated Learning](https://mlsanity.com/paper/2302.12559/) (2023)
- [Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees](https://mlsanity.com/paper/2601.07665/) (2026)
- [A regret minimization approach to fixed-point iterations](https://mlsanity.com/paper/2509.21653/) (2025)

## Abstract (arXiv)

Many popular first order algorithms for convex optimization, such as forward-backward splitting, Douglas-Rachford splitting, and the alternating direction method of multipliers (ADMM), can be formulated as averaged iteration of a nonexpansive mapping. In this paper we propose a line search for averaged iteration that preserves the theoretical convergence guarantee, while often accelerating practical convergence. We discuss several general cases in which the additional computational cost of the line search is modest compared to the savings obtained.