On inexact ADMMs with relative error criteria

doi:10.1007/s10589-018-0022-2

	On inexact ADMMs with relative error criteria
	Xie, Jiaxin
刊名	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
	2018-12-01
卷号	71 期号:3 页码:743-765
关键词	Alternating direction method of multipliers (ADMM) Inexactness Relative error criteria Large step-length
ISSN号	0926-6003
DOI	10.1007/s10589-018-0022-2
英文摘要	In this paper, we develop two inexact alternating direction methods of multipliers (ADMMs) with relative error criteria for which only a few parameters are needed to control the error tolerance. In many practical applications, the numerical performance is often improved if a larger step-length is used. Hence in this paper we also consider to seek a larger step-length to update the Lagrangian multiplier for better numerical efficiency. Specifically, if we only allow one subproblem in the classic ADMM to be solved inexactly by a certain relative error criterion, then a larger step-length can be used to update the Lagrangian multiplier. Related convergence analysis of those proposed algorithms is also established under the assumption that the solution set to the KKT system of the problem is not empty. Numerical experiments on solving total variation (TV)-based image denosing and analysis sparse recovery problems are provided to demonstrate the effectiveness of the proposed methods and the advantage of taking a larger step-length.
资助项目	China Postdoctoral Science Foundation[2017LH043] ; China Postdoctoral Science Foundation[2017M620938]
WOS研究方向	Operations Research & Management Science ; Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000451340000005
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/31783]
专题	中国科学院数学与系统科学研究院
通讯作者	Xie, Jiaxin
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Xie, Jiaxin. On inexact ADMMs with relative error criteria[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2018,71(3):743-765.
APA	Xie, Jiaxin.(2018).On inexact ADMMs with relative error criteria.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,71(3),743-765.
MLA	Xie, Jiaxin."On inexact ADMMs with relative error criteria".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 71.3(2018):743-765.