  The mirror descent algorithm (MDA) generalizes gradient descent by using a
Bregman divergence to replace squared Euclidean distance. In this paper, we
similarly generalize the alternating direction method of multipliers (ADMM) to
Bregman ADMM (BADMM), which allows the choice of different Bregman divergences
to exploit the structure of problems. BADMM provides a unified framework for
ADMM and its variants, including generalized ADMM, inexact ADMM and Bethe ADMM.
  We establish the global convergence and the $O(1/T)$ iteration complexity for
BADMM. In some cases, BADMM can be faster than ADMM by a factor of
$O(n/\log(n))$. In solving the linear program of mass transportation problem,
BADMM leads to massive parallelism and can easily run on GPU. BADMM is several
times faster than highly optimized commercial software Gurobi.
