ON CONVERGENCE RATE OF DISTRIBUTED STOCHASTIC GRADIENT ALGORITHM FOR CONVEX OPTIMIZATION WITH INEQUALITY CONSTRAINTS

doi:10.1137/15M1048896

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	ON CONVERGENCE RATE OF DISTRIBUTED STOCHASTIC GRADIENT ALGORITHM FOR CONVEX OPTIMIZATION WITH INEQUALITY CONSTRAINTS
	Yuan, Deming 1; Ho, Daniel W. C.2; Hong, Yiguang3
	2016
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	54 期号:5 页码:2872-2892
摘要	In this paper, we consider an optimization problem, where multiple agents cooperate to minimize the sum of their local individual objective functions subject to a global inequality constraint. We propose a class of distributed stochastic gradient algorithms that solve the problem using only local computation and communication. The implementation of the algorithms removes the need for performing the intermediate projections. For strongly convex optimization, we employ a smoothed constraint incorporation technique to show that the algorithm converges at an expected rate of O(In T/T) (where T is the number of iterations) with bounded gradients. For non-strongly convex optimization, we use a reduction technique to establish an O(1/root T) convergence rate in expectation. Finally, a numerical example is provided to show the convergence of the proposed algorithms.
关键词	distributed convex optimization constrained optimization algorithm stochastic gradient convergence rate
DOI	10.1137/15M1048896
语种	英语
资助项目	National Natural Science Foundation of China[61304042] ; National Natural Science Foundation of China[61573344] ; HKSAR[CityU 11204514] ; HKSAR[CityU 11300415] ; Natural Science Foundation of Jiangsu Province[BK20130856]
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000387323500026
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24055
专题	系统科学研究所
通讯作者	Yuan, Deming
作者单位	1.Nanjing Univ Posts & Telecommun, Coll Automat, Nanjing 210023, Jiangsu, Peoples R China 2.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Yuan, Deming,Ho, Daniel W. C.,Hong, Yiguang. ON CONVERGENCE RATE OF DISTRIBUTED STOCHASTIC GRADIENT ALGORITHM FOR CONVEX OPTIMIZATION WITH INEQUALITY CONSTRAINTS[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2016,54(5):2872-2892.
APA	Yuan, Deming,Ho, Daniel W. C.,&Hong, Yiguang.(2016).ON CONVERGENCE RATE OF DISTRIBUTED STOCHASTIC GRADIENT ALGORITHM FOR CONVEX OPTIMIZATION WITH INEQUALITY CONSTRAINTS.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,54(5),2872-2892.
MLA	Yuan, Deming,et al."ON CONVERGENCE RATE OF DISTRIBUTED STOCHASTIC GRADIENT ALGORITHM FOR CONVEX OPTIMIZATION WITH INEQUALITY CONSTRAINTS".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 54.5(2016):2872-2892.