Convergence of an asynchronous block-coordinate forward-backward algorithm for convex composite optimization

0Citations
Citations of this article
3Readers
Mendeley users who have this article in their library.

This article is free to access.

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-Fejér 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. Under the same condition strong convergence of the iterates is provided as well as their linear convergence rate.

Cite

CITATION STYLE

APA

Traoré, C., Salzo, S., & Villa, S. (2023). Convergence of an asynchronous block-coordinate forward-backward algorithm for convex composite optimization. Computational Optimization and Applications, 86(1), 303–344. https://doi.org/10.1007/s10589-023-00489-w

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free