  We consider constraint-coupled optimization problems in which agents of a
network aim to cooperatively minimize the sum of local objective functions
subject to individual constraints and a common linear coupling constraint. We
propose a novel optimization algorithm that embeds a dynamic average consensus
protocol in the parallel Alternating Direction Method of Multipliers (ADMM) to
design a fully distributed scheme for the considered set-up. The dynamic
average mechanism allows agents to track the time-varying coupling constraint
violation (at the current solution estimates). The tracked version of the
constraint violation is then used to update local dual variables in a
consensus-based scheme mimicking a parallel ADMM step. Under convexity, we
prove that all limit points of the agents' primal solution estimates form an
optimal solution of the constraint-coupled (primal) problem. The result is
proved by means of a Lyapunov-based analysis simultaneously showing consensus
of the dual estimates to a dual optimal solution, convergence of the tracking
scheme and asymptotic optimality of primal iterates. A numerical study on
optimal charging schedule of plug-in electric vehicles corroborates the
theoretical results.
