Combining ADMM and tracking over networks for distributed constraint-coupled optimization

In this paper, we propose a novel distributed algorithm to address constraint-coupled optimization problems in which agents in a network aim at cooperatively minimizing the sum of local objective functions subject to individual constraints and a common, linear coupling constraint. Our optimization scheme embeds a dynamic average consensus protocol in the (parallel) Alternating Direction Method of Multipliers (ADMM) to design a fully distributed algorithm. More precisely, the dual variable update step of the master node in ADMM is now performed locally by the agent, which update their own copy of the dual variable in a consensus-based scheme using a dynamic average mechanism to track the coupling constraint violation. Under convexity, we show convergence of the primal solution estimates to an optimal solution of the constraint-coupled target problem. A numerical example supports the theoretical results.