Graph balancing for distributed subgradient methods over directed graphs
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Ozdaglar_Graph balancing.pdf
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Author(s)
Makhdoumi Kakhaki, Ali
Koksal, Asuman E.
Date Issued
February 2016
Journal
2015 54th IEEE Conference on Decision and Control (CDC)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Makhdoumi, Ali, and Ozdaglar, Asuman. “Graph Balancing for Distributed Subgradient Methods over Directed Graphs.” 2015 54th IEEE Conference on Decision and Control (CDC), December 15-18 2015, Osaka, Japan, Institute of Electrical and Electronics Engineers (IEEE), February 2016: 1364-1371 © 2015 Institute of Electrical and Electronics Engineers (IEEE)
Version
Author's final manuscript
Abstract
We consider a multi agent optimization problem where a set of agents collectively solves a global optimization problem with the objective function given by the sum of locally known convex functions. We focus on the case when information exchange among agents takes place over a directed network and propose a distributed subgradient algorithm in which each agent performs local processing based on information obtained from his incoming neighbors. Our algorithm uses weight balancing to overcome the asymmetries caused by the directed communication network, i.e., agents scale their outgoing information with dynamically updated weights that converge to balancing weights of the graph. We show that both the objective function values and the consensus violation, at the ergodic average of the estimates generated by the algorithm, converge with rate equation, where T is the number of iterations. A special case of our algorithm provides a new distributed method to compute average consensus over directed graphs.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/CDC.2015.7402401
