A randomized dual consensus ADMM method for multi-agent distributed optimization

Recently, the alternating direction method of multipliers (ADMM) has been used for distributed consensus optimization and is shown to converge faster than conventional approaches based on consensus subgradient. In this paper, we consider a convex optimization problem with a linearly coupled equality constraint and employ a dual consensus ADMM (DC-ADMM) method for solving the problem in a fully distributed fashion. In particular, by considering a non-ideal network where the agents can be ON and OFF randomly and the communications among agents can fail probabilistically, we propose a randomized DC-ADMM method that is robust against these non-ideal effects. Moreover, we show that the proposed randomized method is provably convergent to an optimal solution and has a worst-case O(1/k) convergence rate, where k is the iteration number. Simulation results are presented to examine the practical convergence behavior of the proposed method in the presence of randomly ON/OFF agents and non-ideal communication links.