Distributed Optimization Using the Primal-Dual Method of Multipliers

Zhang, G; Heusdens, R

Distributed Optimization Using the Primal-Dual Method of Multipliers

Zhang, G

Heusdens, R

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Signal and Information Processing over Networks, 2018, 4 (1), pp. 173 - 187
Issue Date:: 2018-03-01

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Field	Value	Language
dc.contributor.author	Zhang, G https://orcid.org/0000-0003-4521-542X	en_US
dc.contributor.author	Heusdens, R	en_US
dc.date.available	2020-05-25T19:04:37Z
dc.date.issued	2018-03-01	en_US
dc.identifier.citation	IEEE Transactions on Signal and Information Processing over Networks, 2018, 4 (1), pp. 173 - 187	en_US
dc.identifier.uri	http://hdl.handle.net/10453/131402
dc.description.abstract	© 2015 IEEE. In this paper, we propose the primal-dual method of multipliers (PDMM) for distributed optimization over a graph. In particular, we optimize a sum of convex functions defined over a graph, where every edge in the graph carries a linear equality constraint. In designing the new algorithm, an augmented primal-dual Lagrangian function is constructed which smoothly captures the graph topology. It is shown that a saddle point of the constructed function provides an optimal solution of the original problem. Further under both the synchronous and asynchronous updating schemes, PDMM has the convergence rate of O(1/K) (where K denotes the iteration index) for general closed, proper, and convex functions. Other properties of PDMM such as convergence speeds versus different parameter-settings and resilience to transmission failure are also investigated through the experiments of distributed averaging.	en_US
dc.relation.ispartof	IEEE Transactions on Signal and Information Processing over Networks	en_US
dc.relation.isbasedon	10.1109/TSIPN.2017.2672403	en_US
dc.title	Distributed Optimization Using the Primal-Dual Method of Multipliers	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	4	en_US
utslib.for	0805 Distributed Computing	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	open_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	4	en_US

Abstract:

© 2015 IEEE. In this paper, we propose the primal-dual method of multipliers (PDMM) for distributed optimization over a graph. In particular, we optimize a sum of convex functions defined over a graph, where every edge in the graph carries a linear equality constraint. In designing the new algorithm, an augmented primal-dual Lagrangian function is constructed which smoothly captures the graph topology. It is shown that a saddle point of the constructed function provides an optimal solution of the original problem. Further under both the synchronous and asynchronous updating schemes, PDMM has the convergence rate of O(1/K) (where K denotes the iteration index) for general closed, proper, and convex functions. Other properties of PDMM such as convergence speeds versus different parameter-settings and resilience to transmission failure are also investigated through the experiments of distributed averaging.

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http://hdl.handle.net/10453/131402