  This paper presents optimal scaling of the alternating directions method of
multipliers (ADMM) algorithm for a class of distributed quadratic programming
problems. The scaling corresponds to the ADMM step-size and relaxation
parameter, as well as the edge-weights of the underlying communication graph.
We optimize these parameters to yield the smallest convergence factor of the
algorithm. Explicit expressions are derived for the step-size and relaxation
parameter, as well as for the corresponding convergence factor. Numerical
simulations justify our results and highlight the benefits of optimally scaling
the ADMM algorithm.
