KMS Of Academy of mathematics and systems sciences, CAS
| On inexact ADMMs with relative error criteria | |
| Xie, Jiaxin | |
| 2018-12-01 | |
| Source Publication | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
 |
| ISSN | 0926-6003 |
| Volume | 71Issue:3Pages:743-765 |
| Abstract | 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. |
| Keyword | Alternating direction method of multipliers (ADMM) Inexactness Relative error criteria Large step-length |
| DOI | 10.1007/s10589-018-0022-2 |
| Language | 英语 |
| Funding Project | China Postdoctoral Science Foundation[2017LH043] ; China Postdoctoral Science Foundation[2017M620938] |
| WOS Research Area | Operations Research & Management Science ; Mathematics |
| WOS Subject | Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000451340000005 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31784 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Xie, Jiaxin |
| Affiliation | Chinese 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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