We consider the consensual distributed optimization problem and propose an asynchronous version of the Alternating Direction Method of Multipliers (ADMM) algorithm to solve it. The `asynchronous' part here refers to the fact that only one node/processor is updated (i.e. performs a minimization step) at each iteration of the algorithm. The selection of the node to be updated is decided by simulating a Markov chain. The proposed algorithm is shown to have a linear convergence property in expectation for the class of functions which are strongly convex and continuously differentiable.
@article{arxiv.1810.05067,
title = {Linearly Convergent Asynchronous Distributed ADMM via Markov Sampling},
author = {Suhail M. Shah and Konstantin E. Avrachenkov},
journal= {arXiv preprint arXiv:1810.05067},
year = {2022}
}