In this paper, we review the parallel and distributed optimization algorithmsbased on the alternating direction method of multipliers (ADMM) for solving"big data" optimization problems in modern communication networks. We firstintroduce the canonical formulation of the large-scale optimization problem.Next, we describe the general form of ADMM and then focus on several directextensions and sophisticated modifications of ADMM from $2$-block to $N$-blocksettings to deal with the optimization problem. The iterative schemes andconvergence properties of each extension/modification are given, and theimplementation on large-scale computing facilities is also illustrated.Finally, we numerate several applications in communication networks, such asthe security constrained optimal power flow problem in smart grid networks andmobile data offloading problem in software defined networks (SDNs).
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机译：在本文中，我们回顾了基于乘法器交替方向方法（ADMM）的并行和分布式优化算法，用于解决现代通信网络中的“大数据”优化问题。我们首先介绍大规模优化问题的规范表述，然后介绍ADMM的一般形式，然后重点介绍ADMM的几种直接扩展和复杂的修改，从$ 2 $块到$ N $块设置以处理优化问题。给出了每个扩展/修改的迭代方案和收敛特性，并说明了在大型计算设备上的实现。最后，我们列举了通信网络中的几种应用，例如智能电网中安全受限的最优潮流问题和移动数据卸载。软件定义网络（SDN）中出现问题。
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