  Distributed optimization aims to optimize a global objective formed by a sum
of coupled local convex functions over a graph via only local computation and
communication. In this paper, we propose the Bregman parallel direction method
of multipliers (PDMM) based on a generalized averaging step named mirror
averaging. We establish the global convergence and $O(1/T)$ convergence rate of
the Bregman PDMM, along with its $O(n/\ln n)$ improvement over existing PDMM,
where $T$ denotes the number of iterations and $n$ the dimension of solution
variable. In addition, we can enhance its performance by optimizing the
spectral gap of the averaging matrix. We demonstrate our results via a
numerical example.
