Convergence of an Asynchronous Block-Coordinate Forward-Backward Algorithm for Convex Composite Optimization
Optimization and Control
2023-04-14 v2 Distributed, Parallel, and Cluster Computing
Abstract
In this paper, we study the convergence properties of a randomized block-coordinate descent algorithm for the minimization of a composite convex objective function, where the block-coordinates are updated asynchronously and randomly according to an arbitrary probability distribution. We prove that the iterates generated by the algorithm form a stochastic quasi-Fej\'er sequence and thus converge almost surely to a minimizer of the objective function. Moreover, we prove a general sublinear rate of convergence in expectation for the function values and a linear rate of convergence in expectation under an error bound condition of Tseng type.
Cite
@article{arxiv.2201.05498,
title = {Convergence of an Asynchronous Block-Coordinate Forward-Backward Algorithm for Convex Composite Optimization},
author = {Cheik Traoré and Saverio Salzo and Silvia Villa},
journal= {arXiv preprint arXiv:2201.05498},
year = {2023}
}