Asynchronous alternating direction method of multipliers applied to the direct-current optimal power flow problem

In a large network of agents, we consider a distributed convex optimization problem where each agent has a private convex cost function and a set of local variables. We provide an algorithm to carry out a multi-area decentralized optimization in an asynchronous fashion, obtained by applying random Gauss-Seidel iterations on the Douglas-Rachford splitting operator. As an application, a direct-current linear optimal power flow model is implemented and simulations results confirm the convergence of the proposed algorithm.