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A distributed Newton method for Network Utility Maximization

Author(s)
Wei, Ermin; Ozdaglar, Asuman E.; Jadbabaie, Ali
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Abstract
Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative distributed Newton-type fast converging algorithm for solving network utility maximization problems with self-concordant utility functions. By using novel matrix splitting techniques, both primal and dual updates for the Newton step can be computed using iterative schemes in a decentralized manner with limited scalar information exchange. Similarly, the stepsize can be obtained via an iterative consensus-based averaging scheme. We show that even when the Newton direction and the stepsize in our method are computed within some error (due to finite truncation of the iterative schemes), the resulting objective function value still converges superlinearly to an explicitly characterized error neighborhood. Simulation results demonstrate significant convergence rate improvement of our algorithm relative to the existing subgradient methods based on dual decomposition.
Date issued
2010-12
URI
http://hdl.handle.net/1721.1/62146
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
Proceedings of the 2010 49th IEEE Conference on Decision and Control (CDC)
Publisher
Institute of Electrical and Electronics Engineers
Citation
Wei, E., A. Ozdaglar, and A. Jadbabaie. “A distributed Newton method for Network Utility Maximization.” Decision and Control (CDC), 2010 49th IEEE Conference on. 2010. 1816-1821. © Copyright 2010 IEEE
Version: Final published version
ISBN
978-1-4244-7745-6
ISSN
0743-1546

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