Graph balancing for distributed subgradient methods over directed graphs
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 p...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2017
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| Online Access: | http://hdl.handle.net/1721.1/111685 https://orcid.org/0000-0002-1827-1285 |
| _version_ | 1811084680736276480 |
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| author | Makhdoumi Kakhaki, Ali Koksal, Asuman E. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Makhdoumi Kakhaki, Ali Koksal, Asuman E. |
| author_sort | Makhdoumi Kakhaki, Ali |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:55:22Z |
| format | Article |
| id | mit-1721.1/111685 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:55:22Z |
| publishDate | 2017 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1116852022-10-01T11:56:59Z Graph balancing for distributed subgradient methods over directed graphs Makhdoumi Kakhaki, Ali Koksal, Asuman E. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Makhdoumi Kakhaki, Ali Koksal, Asuman E. 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. 2017-10-03T18:58:05Z 2017-10-03T18:58:05Z 2016-02 Article http://purl.org/eprint/type/ConferencePaper 978-1-4799-7886-1 http://hdl.handle.net/1721.1/111685 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) https://orcid.org/0000-0002-1827-1285 en_US http://dx.doi.org/10.1109/CDC.2015.7402401 2015 54th IEEE Conference on Decision and Control (CDC) Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) MIT Web Domain |
| spellingShingle | Makhdoumi Kakhaki, Ali Koksal, Asuman E. Graph balancing for distributed subgradient methods over directed graphs |
| title | Graph balancing for distributed subgradient methods over directed graphs |
| title_full | Graph balancing for distributed subgradient methods over directed graphs |
| title_fullStr | Graph balancing for distributed subgradient methods over directed graphs |
| title_full_unstemmed | Graph balancing for distributed subgradient methods over directed graphs |
| title_short | Graph balancing for distributed subgradient methods over directed graphs |
| title_sort | graph balancing for distributed subgradient methods over directed graphs |
| url | http://hdl.handle.net/1721.1/111685 https://orcid.org/0000-0002-1827-1285 |
| work_keys_str_mv | AT makhdoumikakhakiali graphbalancingfordistributedsubgradientmethodsoverdirectedgraphs AT koksalasumane graphbalancingfordistributedsubgradientmethodsoverdirectedgraphs |