Regularized Primal-Dual Subgradient Method for Distributed Constrained Optimization

In this paper, we study the distributed constrained optimization problem where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint. To solve this problem, we propose a consensus-based distributed regularized pr...

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Published in:	IEEE transactions on cybernetics Vol. 46; no. 9; pp. 2109 - 2118
Main Authors:	Deming Yuan, Ho, Daniel W. C., Shengyuan Xu
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.09.2016 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Average consensus constrained optimization Convergence Convex functions Cost function Cybernetics distributed optimization Lagrangian functions Linear programming primal–dual subgradient method
ISSN:	2168-2267, 2168-2275
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Abstract	In this paper, we study the distributed constrained optimization problem where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint. To solve this problem, we propose a consensus-based distributed regularized primal-dual subgradient method. In contrast to the existing methods, most of which require projecting the estimates onto the constraint set at every iteration, only one projection at the last iteration is needed for our proposed method. We establish the convergence of the method by showing that it achieves an O(K -1/4 ) convergence rate for general distributed constrained optimization, where K is the iteration counter. Finally, a numerical example is provided to validate the convergence of the propose method.
AbstractList	In this paper, we study the distributed constrained optimization problem where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint. To solve this problem, we propose a consensus-based distributed regularized primal-dual subgradient method. In contrast to the existing methods, most of which require projecting the estimates onto the constraint set at every iteration, only one projection at the last iteration is needed for our proposed method. We establish the convergence of the method by showing that it achieves an O(K -1/4 ) convergence rate for general distributed constrained optimization, where K is the iteration counter. Finally, a numerical example is provided to validate the convergence of the propose method. In this paper, we study the distributed constrained optimization problem where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint. To solve this problem, we propose a consensus-based distributed regularized primal-dual subgradient method. In contrast to the existing methods, most of which require projecting the estimates onto the constraint set at every iteration, only one projection at the last iteration is needed for our proposed method. We establish the convergence of the method by showing that it achieves an [Formula Omitted] convergence rate for general distributed constrained optimization, where [Formula Omitted] is the iteration counter. Finally, a numerical example is provided to validate the convergence of the propose method.
Author	Ho, Daniel W. C. Shengyuan Xu Deming Yuan
Author_xml	– sequence: 1 surname: Deming Yuan fullname: Deming Yuan email: dmyuan1012@gmail.com organization: Coll. of Autom., Nanjing Univ. of Posts & Telecommun., Nanjing, China – sequence: 2 givenname: Daniel W. C. surname: Ho fullname: Ho, Daniel W. C. email: madaniel@cityu.edu.hk organization: Dept. of Math., City Univ. of Hong Kong, Hong Kong, China – sequence: 3 surname: Shengyuan Xu fullname: Shengyuan Xu email: syxu@njust.edu.cn organization: Sch. of Autom., Nanjing Univ. of Sci. & Technol., Nanjing, China
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/26285232$$D View this record in MEDLINE/PubMed
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Cites_doi	10.1103/PhysRevE.80.066121 10.1109/TCNS.2014.2357513 10.1109/TAC.2004.834113 10.1109/TAC.2014.2298712 10.1109/TAC.2014.2309261 10.1109/TAC.2011.2167817 10.1109/TAC.2012.2228038 10.1145/1390156.1390191 10.1109/CDC.2008.4739339 10.1109/TAC.2011.2160020 10.1109/TSMCB.2009.2023509 10.1109/TAC.2003.812781 10.1109/TSMC.2014.2332306 10.1109/TAC.2014.2308612 10.1109/TNNLS.2014.2336806 10.1109/TCYB.2015.2398892 10.1109/CDC.2008.4738860 10.1109/TII.2012.2219061 10.1109/TIT.2006.874516 10.1109/TCYB.2014.2366204 10.1109/TSMCB.2011.2160394 10.1109/TAC.1986.1104412 10.1016/j.sysconle.2004.02.022 10.1109/TAC.2010.2041686 10.1109/TSP.2012.2198470 10.1109/TAC.2013.2275671 10.1109/TAC.2011.2161027 10.1109/TAC.2005.846556 10.1007/s10957-010-9737-7 10.1109/TAC.2008.2009515
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References	duchi (ref30) 2008 ref12 ref15 ref14 mahdavi (ref6) 2012; 25 ref33 ref11 ref32 ref10 ref1 ref19 ref18 tsitsiklis (ref2) 1984 lu (ref13) 2010; 40 ref24 ref23 ref26 ref25 ref20 ref22 ref21 ram (ref16) 2010; 147 ref28 ref27 zhu (ref17) 2012; 57 ref29 ref8 ref7 ref9 ref4 ref3 ref5 meng (ref31) 2014; 44
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SubjectTerms	Average consensus constrained optimization Convergence Convex functions Cost function Cybernetics distributed optimization Lagrangian functions Linear programming primal–dual subgradient method
Title	Regularized Primal-Dual Subgradient Method for Distributed Constrained Optimization
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