  Distributed radio interferometric calibration based on consensus optimization
has been shown to improve the estimation of systematic errors in radio
astronomical observations. The intrinsic continuity of systematic errors across
frequency is used by a consensus polynomial to penalize traditional
calibration. Consensus is achieved via the use of alternating direction method
of multipliers (ADMM) algorithm. In this paper, we extend the existing
distributed calibration algorithms to use ADMM with an adaptive penalty
parameter update. Compared to a fixed penalty, its adaptive update has been
shown to perform better in diverse applications of ADMM. In this paper, we
compare two such popular penalty parameter update schemes: residual balance
penalty update and spectral penalty update (Barzilai-Borwein). We apply both
schemes to distributed radio interferometric calibration and compare their
performance against ADMM with a fixed penalty parameter. Simulations show that
both methods of adaptive penalty update improve the convergence of ADMM but the
spectral penalty parameter update shows more stability.
