  In this paper, we review the parallel and distributed optimization algorithms
based on alternating direction method of multipliers (ADMM) for solving "big
data" optimization problem in smart grid communication networks. We first
introduce the canonical formulation of the large-scale optimization problem.
Next, we describe the general form of ADMM and then focus on several direct
extensions and sophisticated modifications of ADMM from $2$-block to $N$-block
settings to deal with the optimization problem. The iterative schemes and
convergence properties of each extension/modification are given, and the
implementation on large-scale computing facilities is also illustrated.
Finally, we numerate several applications in power system for distributed
robust state estimation, network energy management and security constrained
optimal power flow problem.
