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.
@article{arxiv.1303.6680,
title = {Optimal scaling of the ADMM algorithm for distributed quadratic programming},
author = {André Teixeira and Euhanna Ghadimi and Iman Shames and Henrik Sandberg and Mikael Johansson},
journal= {arXiv preprint arXiv:1303.6680},
year = {2016}
}
Comments
Submitted to the IEEE Transactions on Signal Processing. Prior work was presented at the 52nd IEEE Conference on Decision and Control, 2013