Due to the limited energy of sensor nodes in wireless sensor networks, extending the networks lifetime is a major challenge that can be formulated as an optimization problem. In this paper, we propose a distributed iterative algorithm based on Alternating Direction Method of Multipliers (ADMM) with the aim of maximizing sensor network lifetime. The features of this algorithm are use of local information, low overhead of message passing, low computational complexity, fast convergence, and consequently reduced energy consumption. In this study, we present the convergence results and the number of iterations required to achieve the stopping criterion. Furthermore, the impact of problem size (number of sensor nodes) on the solution and constraints violation is studied and finally, the proposed algorithm is compared to one of the well-known subgradient-based algorithms.
 In next generation wireless mobile networks, network virtualization will become an important key technology. In this paper, we firstly propose a resource allocation scheme for enabling efficient resource allocation in wireless network virtualization. Then, we formulate the resource allocation strategy as an optimization problem, considering not only the revenue earned by serving end users of virtual networks, but also the cost of leasing infrastructure from infrastructure providers. In addition, we develop an efficient alternating direction method of multipliers (ADMM)-based distributed virtual resource allocation algorithm in virtualized wireless networks. Simulation results are presented to show the effectiveness of the proposed scheme. We consider a distributed total transmit power minimization in a multi-hop single-sink data gathering wireless sensor network by jointly optimizing the resource allocation and the routing with given source rates. An inherent coupling in optimal routing and resource allocation is taken into account via cross-layer optimization to increase the energy efficiency of the network. Instead of distributing the solution process horizontally by commonly used dual decomposition, we apply consensus optimization in conjunction with the alternating direction method of multipliers (ADMM). By duplicating flow variables, the problem decomposes into node specific subproblems with local variables. These variables are iteratively driven into consensus via the ADMM. Numerical examples show that the proposed algorithm converges significantly faster as compared to the state of the art methods based on the dual decomposition. Additionally, the algorithm is appealing for practical implementation due to its low local communication overhead, robust operation in slightly changing channel conditions and scalability to large networks. This paper develops the application of the alternating direction method of multipliers (ADMM) to optimize a dynamic objective function in a decentralized multi-agent system. At each time slot, agents in the network observe local functions and cooperate to track the optimal time-varying argument of the sum objective. This cooperation is based on maintaining local primal variables that estimate the value of the optimal argument and auxiliary dual variables that encourage proximity with neighboring estimates. Primal and dual variables are updated by an ADMM iteration that can be implemented in a distributed manner whereby local updates require access to local variables and the most recent primal variables from adjacent agents. For objective functions that are strongly convex and have Lipschitz continuous gradients, the distances between the primal and dual iterates to their corresponding time-varying optimal values are shown to converge to a steady state gap. This gap is explicitly characterized in terms of the condition number of the objective function, the condition number of the network that is defined as the ratio between the largest and smallest nonzero Laplacian eigenvalues, and a bound on the drifts of the optimal primal variables and the optimal gradients. Numerical experiments corroborate theoretical findings and show that the results also hold for non-differentiable and non-strongly convex primal objectives.