Distributed Consensus Optimization via ADMM-Tracking

In this paper, we propose a novel distributed algorithm for consensus optimization over networks. The key idea is to achieve dynamic consensus on the agents' average and on the global descent direction by iteratively solving an online auxiliary optimization problem through the Alternating Direction Method of Multipliers (ADMM). Such a mechanism is suitably interlaced with a local proportional action steering each agent estimate to the solution of the original consensus optimization problem. The analysis uses tools from system theory to prove the linear convergence of the scheme with strongly convex costs. Finally, some numerical simulations confirm our findings and show the robustness of the proposed scheme.