A Newton-Like Optimal Resource Allocation Algorithm and its Convergence for Wireless Ad Hoc Networks

For convenience of formulating utilization and fairness, the resource allocation in wireless ad hoc networks is often transformed into a network utility maximization (NUM) problem. However, most existing works cannot involve the convergence speed of resource allocation algorithm which is very important in dynamic environments. So in this paper, we propose a novel resource allocation algorithm, named fast scaled gradient projection algorithm (FSGPA), which has fast convergence speed while maintaining optimal utility and fairness. FSGPA may be viewed as a version of projected Newton method to solve the dual form of the NUM problem, where the diagonal scaling matrix approximates the diagonal terms of the Hessian matrix so that it can be computed at individual cliques of mutual interfering links using local information. In order to validate our methods, two kinds of network settings are considered, i.e., the synchronous network setting and a partial asynchronous network setting. The convergence of the continuous-time system model of FSGPA in the synchronous network setting is proven based on the LaSalle’s theorem. In the meantime, the convergence of discrete-time models of FSGPA in both synchronous and asynchronous network settings is also proven. Finally, both the theoretical and experimental results show that FSGPA performs better than the existing works.