Convergence Analysis of the Relaxed Proximal Point Algorithm
Recently, a worst-case convergence rate was established for the Douglas-Rachford alternating direction method of multipliers (ADMM) in an ergodic sense. The relaxed proximal point algorithm (PPA) is a generalization of the original PPA which includes the Douglas-Rachford ADMM as a special case. In...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/912846 |
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| _version_ | 1849306524749398016 |
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| author | Min Li Yanfei You |
| author_facet | Min Li Yanfei You |
| author_sort | Min Li |
| collection | DOAJ |
| description | Recently, a worst-case convergence rate was established for the Douglas-Rachford alternating direction method of multipliers (ADMM) in an ergodic sense. The relaxed proximal point algorithm (PPA) is a generalization of the original PPA which includes the Douglas-Rachford ADMM as a special case. In this paper, we provide a simple proof for the same convergence rate of the relaxed PPA in both ergodic and nonergodic senses. |
| format | Article |
| id | doaj-art-2cd937d833964a659ecd2ba3cf28a99b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2cd937d833964a659ecd2ba3cf28a99b2025-08-20T03:55:02ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/912846912846Convergence Analysis of the Relaxed Proximal Point AlgorithmMin Li0Yanfei You1School of Economics and Management, Southeast University, Nanjing 210096, ChinaDepartment of Mathematics, Nanjing University, Nanjing 210093, ChinaRecently, a worst-case convergence rate was established for the Douglas-Rachford alternating direction method of multipliers (ADMM) in an ergodic sense. The relaxed proximal point algorithm (PPA) is a generalization of the original PPA which includes the Douglas-Rachford ADMM as a special case. In this paper, we provide a simple proof for the same convergence rate of the relaxed PPA in both ergodic and nonergodic senses.http://dx.doi.org/10.1155/2013/912846 |
| spellingShingle | Min Li Yanfei You Convergence Analysis of the Relaxed Proximal Point Algorithm Abstract and Applied Analysis |
| title | Convergence Analysis of the Relaxed Proximal Point Algorithm |
| title_full | Convergence Analysis of the Relaxed Proximal Point Algorithm |
| title_fullStr | Convergence Analysis of the Relaxed Proximal Point Algorithm |
| title_full_unstemmed | Convergence Analysis of the Relaxed Proximal Point Algorithm |
| title_short | Convergence Analysis of the Relaxed Proximal Point Algorithm |
| title_sort | convergence analysis of the relaxed proximal point algorithm |
| url | http://dx.doi.org/10.1155/2013/912846 |
| work_keys_str_mv | AT minli convergenceanalysisoftherelaxedproximalpointalgorithm AT yanfeiyou convergenceanalysisoftherelaxedproximalpointalgorithm |