# Stochastic Quasi-Fej'er Block-Coordinate Fixed Point Iterations With Random Sweeping II: Mean-Square and Linear Convergence

arXiv: https://arxiv.org/abs/1704.08083 · HTML: https://mlsanity.com/paper/1704.08083/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2017.

## 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)
- [An abstract effective convergence theorem for stochastic processes, with applications to stochastic approximation](https://mlsanity.com/paper/2504.12922/) (2025)
- [Mean-square and sublinear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature](https://mlsanity.com/paper/2510.10697/) (2025)

## Abstract (arXiv)

Reference [11] investigated the almost sure weak convergence of block-coordinate fixed point algorithms and discussed their applications to nonlinear analysis and optimization. This algorithmic framework features random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and it allows for stochastic errors in the evaluation of the operators. The present paper establishes results on the mean-square and linear convergence of the iterates. Applications to monotone operator splitting and proximal optimization algorithms are presented.