Abstract : This paper investigates a method to distributively solve a Network Utility Maximization (NUM) problem with coupled variables and applies it to study power control in wireless sensor networks (WSNs). We present a dual decomposition-based consistency price algorithm to solve the coupled problem. However, the consistency price algorithm suffers from slow convergence. We then propose a two-step method to address the given issue. The first step is to build up a global consensus problem by introducing slack variables to transform the NUM problem with globally coupled variables into a NUM problem with coupled constraints. The second step is to design a distributed algorithm that combines the first-order gradient/subgradient method and a local consensus algorithm to solve the global consensus problem. The proposed algorithm is a primary algorithm which has faster convergence speed than the consistency price algorithm which is a primary-dual algorithm. Experimental results have demonstrated the effectiveness of our proposed approach.
Index terms : Consensus algorithm, network utility maximization, power control, primary-dual algorithm, wireless sensor networks.