  In this paper, we review the parallel and distributed optimization algorithms
based on the alternating direction method of multipliers (ADMM) for solving
"big data" optimization problems in modern 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 communication networks, such as
the security constrained optimal power flow problem in smart grid networks and
mobile data offloading problem in software defined networks (SDNs).
