Tracking-ADMM for Distributed Constraint-Coupled Optimization

• Main Authors: Falsone, Alessandro, Notarnicola, Ivano, Notarstefano, Giuseppe, Prandini, Maria
• Format: Journal Article
• Language: English
• Published: 25.07.2019
• Subjects: Computer Science - Systems and Control; Mathematics - Optimization and Control
• DOI: 10.48550/arxiv.1907.10860

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.