On inexact ADMMs with relative error criteria
Xie, Jiaxin
AbstractIn 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.
KeywordAlternating direction method of multipliers (ADMM) Inexactness Relative error criteria Large step-length
Funding ProjectChina Postdoctoral Science Foundation[2017LH043] ; China Postdoctoral Science Foundation[2017M620938]
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000451340000005
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Document Type期刊论文
Corresponding AuthorXie, Jiaxin
AffiliationChinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
Recommended Citation
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.
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