Fine tuning consensus optimization for distributed radio interferometric calibration

We recently proposed the use of consensus optimization as a viable and effective way to improve the quality of calibration of radio interferometric data. We showed that it is possible to obtain far more accurate calibration solutions and also to distribute the compute load across a network of computers by using this technique. A crucial aspect in any consensus optimization problem is the selection of the penalty parameter used in the alternating direction method of multipliers (ADMM) iterations. This affects the convergence speed as well as the accuracy. In this paper, we use the Hessian of the cost function used in calibration to appropriately select this penalty. We extend our results to a multi-directional calibration setting, where we propose to use a penalty scaled by the squared intensity of each direction.