Asynchronous Algorithms for Distributed Consensus-Based Optimization and Distributed Resource Allocation over Random Networks

In this paper, distributed consensus-based optimization and network resource allocation problem are considered, where agents make decisions using local information in the presence of random communication topologies. Distributed algorithms are proposed for the two problems such that the algorithms are both asynchronous and totally asynchronous. The algorithms do not require diminishing step sizes and are able to converge almost surely and in mean square without requiring a priori B-connectivity or distribution assumption of switching graphs. The algorithms are able to converge even if weighted matrix of the graph is periodic and irreducible in synchronous protocol. To the best knowledge of the authors, the proposed distributed algorithm for resource allocation is the first algorithm which is both asynchronous and totally asynchronous over random networks. Finally, a numerical example of distributed estimation in wireless sensor networks is provided in order to illustrate the results.