Optimal scaling of the ADMM algorithm for distributed quadratic programming

This paper addresses the optimal scaling of the ADMM method for distributed quadratic programming. Scaled ADMM iterations are first derived for generic equality-constrained quadratic problems and then applied to a class of distributed quadratic problems. In this setting, the scaling corresponds to the step-size and the edge-weights of the underlying communication graph. We optimize the convergence factor of the algorithm with respect to the step-size and graph edge-weights. Explicit analytical expressions for the optimal convergence factor and the optimal step-size are derived. Numerical simulations illustrate our results.