  Due to the rapidly growing scale and heterogeneity of wireless networks, the
design of distributed cross-layer optimization algorithms have received
significant interest from the networking research community. So far, the
standard distributed cross-layer approach in the literature is based on
first-order Lagrangian dual decomposition and the subgradient method, which
suffers 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 interference in wireless networks,
the Hessian matrix of the cross-layer problem has an non-separable structure.
As a result, developing a distributed second-order algorithm is far more
challenging than its counterpart for wireline networks. Our main results in
this paper are two-fold: i) For a special network setting where all links
mutually interfere, we derive decentralized closed-form expressions to compute
the Hessian inverse; ii) For general wireless networks where the interference
relationships are arbitrary, we propose a distributed iterative matrix
splitting scheme for the Hessian inverse. These results successfully lead to a
new theoretical framework for cross-layer optimization in wireless networks.
More importantly, our work contributes to an exciting second-order paradigm
shift in wireless networks optimization theory.
