Optimal scaling of the ADMM algorithm for distributed quadratic programming
Andre Teixeira, Euhanna Ghadimi, Iman Shames, Henrik Sandberg, Mikael Johansson · 2013
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.