Large scale deployment of Internet of Things (IoT) devices poses challenges in resource allocation. In this paper, alternating direction method of multipliers (ADMM) is adopted to solve such large scale resource allocation problems. Based on this, three optimization problems are investigated in a hierarchical IoT network. Considering ADMM could not solve a non-convex optimization problem directly, a non-convex fractional programming problem i.e., energy efficiency maximization problem for IoT region server, is formulated. Faced with this problem, we introduce the Dinkelbach algorithm to transfer the energy efficiency maximization problem into an equivalent convex optimization problem. Then the classic ADMM with two blocks is employed to solve the equivalent convex optimization problem. On the other hand, the classic ADMM with two blocks could not satisfy the convergence speed demands of the high-dimensional convex optimization problems any more. Thus, the network latency minimization problem for controller is designed and then solved by the Jacobian-ADMM algorithm in parallel. It is hard to satisfy controller and IoT region servers’ objectives at the same time. Given this, an incentive mechanism on the basis of Stackelberg game is designed. Thus a game-based resource allocation problem is proposed to deal with the contradiction between the centralized objective of the controller and the individual objectives from the IoT region servers. Based on the Dinkelbach algorithm and Jacobian-ADMM algorithm, a two-layer iterative resource allocation algorithm is posed to solve the game-based resource allocation problem. Last but not least, the convergence of the proposed algorithms are analyzed with numerous simulation results.

中文翻译：

---

基于ADMM的物联网网络大规模资源配置

物联网 (IoT) 设备的大规模部署对资源分配提出了挑战。本文采用乘法器交替方向法（ADMM）来解决此类大规模资源分配问题。在此基础上，研究了分层物联网网络中的三个优化问题。考虑到ADMM不能直接解决非凸优化问题，提出了一个非凸分数式规划问题，即IoT区域服务器的能效最大化问题。面对这个问题，我们引入Dinkelbach算法将能效最大化问题转化为等价的凸优化问题。然后使用具有两个块的经典 ADMM 来解决等效凸优化问题。另一方面，具有两个块的经典 ADMM 已不能满足高维凸优化问题的收敛速度要求。因此，设计了控制器的网络延迟最小化问题，然后通过 Jacobian-ADMM 算法并行求解。很难同时满足控制器和物联网区域服务器的目标。鉴于此，设计了基于 Stackelberg 博弈的激励机制。因此，提出了一个基于游戏的资源分配问题来处理控制器的集中目标与物联网区域服务器的个体目标之间的矛盾。基于Dinkelbach算法和Jacobian-ADMM算法，提出了一种两层迭代资源分配算法来解决基于博弈的资源分配问题。最后但并非最不重要的，