Asynchronous ADMM via a Data Exchange Server

With advances in interprocessing-unit communication technology, distributed algorithms are becoming increasingly advantageous. This article focuses on solving convex distributed optimization problems with local consensus coupling constraints via the alternating direction method of multipliers, by means of an asynchronous methodology allowing for communication delays. We use a bipartite undirected graph to denote the update structure of the processing agents that cooperatively perform the distributed algorithm without a centralized aggregator. We introduce a data server to exchange the asynchronous consensus data among the processing agents. Under certain technical assumptions that involve bounded delays, bounded step sizes, and strong convexities in parts of the local objectives, the running average of the local iterates generated by the proposed asynchronous algorithm converges to an optimal solution.