Distributed Constraint-Coupled Optimization: Harnessing ADMM-consensus for robustness

In this paper, we consider a network of agents that jointly aim to minimise the sum of local functions subject to coupling constraints involving all local variables. To solve this problem, we propose a novel solution based on a primal-dual architecture. The algorithm is derived starting from an alternative definition of the Lagrangian function, and its convergence to the optimal solution is proved using recent advanced results in the theory of time-scale separation in nonlinear systems. The rate of convergence is shown to be linear under standard assumptions on the local cost functions. Interestingly, the algorithm is amenable to a direct implementation to deal with asynchronous communication scenarios that may be corrupted by other non-idealities such as packet loss. We numerically test the validity of our approach on a real-world application related to the provision of ancillary services in three-phase low-voltage microgrids.