Convergence analysis on a modified generalized alternating direction method of multipliers
Abstract The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving convex composite minimization problem. The generalized ADMM relaxes both the variables and the multipliers with a common relaxation factor in (0,2) $(0,2)$, which has the po...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1721-z |
| _version_ | 1811288191331729408 |
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| author | Sha Lu Zengxin Wei |
| author_facet | Sha Lu Zengxin Wei |
| author_sort | Sha Lu |
| collection | DOAJ |
| description | Abstract The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving convex composite minimization problem. The generalized ADMM relaxes both the variables and the multipliers with a common relaxation factor in (0,2) $(0,2)$, which has the potential of enhancing the performance of the classic ADMM. Very recently, two different variants of semi-proximal generalized ADMM have been proposed. They allow the weighting matrix in the proximal terms to be positive semidefinite, which makes the subproblems relatively easy to evaluate. One of the variants of semi-proximal generalized ADMMs has been analyzed theoretically, but the convergence result of the other is not known so far. This paper aims to remedy this deficiency and establish its convergence result under some mild conditions in the sense that the relaxation factor is also restricted into (0,2) $(0,2)$. |
| first_indexed | 2024-04-13T03:32:41Z |
| format | Article |
| id | doaj.art-76f5b21eb33541e69db01520e012a922 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-13T03:32:41Z |
| publishDate | 2018-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-76f5b21eb33541e69db01520e012a9222022-12-22T03:04:25ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-06-012018111410.1186/s13660-018-1721-zConvergence analysis on a modified generalized alternating direction method of multipliersSha Lu0Zengxin Wei1School of Science, East China University of Science and TechnologySchool of Mathematics and Information Science, Guangxi UniversityAbstract The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving convex composite minimization problem. The generalized ADMM relaxes both the variables and the multipliers with a common relaxation factor in (0,2) $(0,2)$, which has the potential of enhancing the performance of the classic ADMM. Very recently, two different variants of semi-proximal generalized ADMM have been proposed. They allow the weighting matrix in the proximal terms to be positive semidefinite, which makes the subproblems relatively easy to evaluate. One of the variants of semi-proximal generalized ADMMs has been analyzed theoretically, but the convergence result of the other is not known so far. This paper aims to remedy this deficiency and establish its convergence result under some mild conditions in the sense that the relaxation factor is also restricted into (0,2) $(0,2)$.http://link.springer.com/article/10.1186/s13660-018-1721-zConvex optimizationAugmented Lagrangian functionAlternating direction method of multipliersSemi-proximal terms |
| spellingShingle | Sha Lu Zengxin Wei Convergence analysis on a modified generalized alternating direction method of multipliers Journal of Inequalities and Applications Convex optimization Augmented Lagrangian function Alternating direction method of multipliers Semi-proximal terms |
| title | Convergence analysis on a modified generalized alternating direction method of multipliers |
| title_full | Convergence analysis on a modified generalized alternating direction method of multipliers |
| title_fullStr | Convergence analysis on a modified generalized alternating direction method of multipliers |
| title_full_unstemmed | Convergence analysis on a modified generalized alternating direction method of multipliers |
| title_short | Convergence analysis on a modified generalized alternating direction method of multipliers |
| title_sort | convergence analysis on a modified generalized alternating direction method of multipliers |
| topic | Convex optimization Augmented Lagrangian function Alternating direction method of multipliers Semi-proximal terms |
| url | http://link.springer.com/article/10.1186/s13660-018-1721-z |
| work_keys_str_mv | AT shalu convergenceanalysisonamodifiedgeneralizedalternatingdirectionmethodofmultipliers AT zengxinwei convergenceanalysisonamodifiedgeneralizedalternatingdirectionmethodofmultipliers |