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Most existing work uses dual decomposition and subgradient methods to solveNetwork Utility Maximization (NUM) problems in a distributed manner, whichsuffer from slow rate of convergence properties. This work develops analternative distributed Newton-type fast converging algorithm for solvingnetwork utility maximization problems with self-concordant utility functions.By using novel matrix splitting techniques, both primal and dual updates forthe Newton step can be computed using iterative schemes in a decentralizedmanner with limited information exchange. Similarly, the stepsize can beobtained via an iterative consensus-based averaging scheme. We show that evenwhen the Newton direction and the stepsize in our method are computed withinsome error (due to finite truncation of the iterative schemes), the resultingobjective function value still converges superlinearly to an explicitlycharacterized error neighborhood. Simulation results demonstrate significantconvergence rate improvement of our algorithm relative to the existingsubgradient methods based on dual decomposition.

A Distributed Newton Method for Network Utility Maximization