A Distributed Newton Method for Network Optimization
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Ozdaglar_A distributed.pdf
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Author(s)
Jadbabaie, Ali
Ozdaglar, Asuman E.
Zargham, Michael
Date Issued
December 2009
Journal
Proceedings of the 48th IEEE Conference on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009
Publisher
Institute of Electrical and Electronics Engineers
Citation
Jadbabaie, A., A. Ozdaglar, and M. Zargham. “A Distributed Newton Method For Network Optimization.” Decision and Control, 2009 Held Jointly With the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings Of the 48th IEEE Conference On. 2009. 2736-2741.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1109/CDC.2009.5400289
