A Distributed Newton Method for Network Optimization

Abstract

Most existing work uses dual decomposition and subgradient methods to solve network optimization problems in a distributed manner, which suffer from slow convergence rate properties. This paper proposes an alternative distributed approach based on a Newton-type method for solving minimum cost network optimization problems. The key component of the method is to represent the dual Newton direction as the solution of a discrete Poisson equation involving the graph Laplacian. This representation enables using an iterative consensus-based local averaging scheme (with an additional input term) to compute the Newton direction based only on local information. We show that even when the iterative schemes used for computing the Newton direction and the stepsize in our method are truncated, the resulting iterates converge superlinearly within an explicitly characterized error neighborhood. Simulation results illustrate the significant performance gains of this method relative to subgradient methods based on dual decomposition.