Synchronous distributed ADMM for consensus convex optimization problems with self-loops

Abstract

In this paper, a distributed algorithm based on the alternating direction method of multipliers is proposed to solve an unconstrained consensus optimization problem. The network topology among the agents is assumed to be connected and self-loops of each agent are considered. This algorithm takes less time than sequential algorithms because the optimization variables of the agents can be updated synchronously. In addition, it is shown that the algorithm is actually a Jacobi-proximal ADMM algorithm and the requirement of the proximal matrix is relaxed. A convergence analysis of the algorithm is provided, and its convergence rate is found to be O(1/k). Finally, the characteristics of the proposed algorithm are illustrated by numerical experiments, and comparisons are made with other ADMM algorithms in solving a least-squares problem.