Distributed cross-layer optimization in wireless networks: A second-order approach

Due to the rapidly growing scale and heterogeneity of wireless networks, the design of distributed cross-layer optimization algorithms has received significant interest from the networking research community. So far, the standard distributed cross-layer approach in the literature is based on the first-order Lagrangian dual decomposition and the subgradient method, which suffers from a slow convergence rate. In this paper, we make the first known attempt to develop a distributed Newton´s method, which is second-order and enjoys a quadratic convergence rate. However, due to the inherent interference in wireless networks, the Hessian matrix of the cross-layer problem has a non-separable structure. As a result, developing a distributed second-order algorithm is far more difficult than its counterpart for wireline networks. Our main contributions in this paper are two-fold: i) For a special network setting where all links mutually interfere, we derive closed-form expressions for the Hessian inverse, which further yield a distributed Newton´s method; ii) For general wireless networks where the interference relationships are arbitrary, we propose a double matrix-splitting scheme, which also leads to a distributed Newton´s method. Collectively, these results create a new theoretical framework for distributed cross-layer optimization in wireless networks. More importantly, our work contributes to a potential second-order paradigm shift in wireless networks optimization theory.