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Article: A proximal point algorithm revisit on the alternating direction method of multipliers
Title | A proximal point algorithm revisit on the alternating direction method of multipliers |
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Authors | |
Keywords | alternating direction method of multipliers proximal point algorithm convex programming convergence rate |
Issue Date | 2013 |
Citation | Science China Mathematics, 2013, v. 56, n. 10, p. 2179-2186 How to Cite? |
Abstract | The alternating direction method of multipliers (ADMM) is a benchmark for solving convex programming problems with separable objective functions and linear constraints. In the literature it has been illustrated as an application of the proximal point algorithm (PPA) to the dual problem of the model under consideration. This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter. This primal illustration of ADMM is thus complemental to its dual illustration in the literature. This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily. A worst-case O(1/t) convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas's generalized ADMM. © 2013 Science China Press and Springer-Verlag Berlin Heidelberg. |
Persistent Identifier | http://hdl.handle.net/10722/250875 |
ISSN | 2023 Impact Factor: 1.4 2023 SCImago Journal Rankings: 1.060 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Cai, Xing Ju | - |
dc.contributor.author | Gu, Guo Yong | - |
dc.contributor.author | He, Bing Sheng | - |
dc.contributor.author | Yuan, Xiao Ming | - |
dc.date.accessioned | 2018-02-01T01:53:57Z | - |
dc.date.available | 2018-02-01T01:53:57Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | Science China Mathematics, 2013, v. 56, n. 10, p. 2179-2186 | - |
dc.identifier.issn | 1674-7283 | - |
dc.identifier.uri | http://hdl.handle.net/10722/250875 | - |
dc.description.abstract | The alternating direction method of multipliers (ADMM) is a benchmark for solving convex programming problems with separable objective functions and linear constraints. In the literature it has been illustrated as an application of the proximal point algorithm (PPA) to the dual problem of the model under consideration. This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter. This primal illustration of ADMM is thus complemental to its dual illustration in the literature. This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily. A worst-case O(1/t) convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas's generalized ADMM. © 2013 Science China Press and Springer-Verlag Berlin Heidelberg. | - |
dc.language | eng | - |
dc.relation.ispartof | Science China Mathematics | - |
dc.subject | alternating direction method of multipliers | - |
dc.subject | proximal point algorithm | - |
dc.subject | convex programming | - |
dc.subject | convergence rate | - |
dc.title | A proximal point algorithm revisit on the alternating direction method of multipliers | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s11425-013-4683-0 | - |
dc.identifier.scopus | eid_2-s2.0-84884416593 | - |
dc.identifier.volume | 56 | - |
dc.identifier.issue | 10 | - |
dc.identifier.spage | 2179 | - |
dc.identifier.epage | 2186 | - |
dc.identifier.isi | WOS:000324514200018 | - |
dc.identifier.issnl | 1869-1862 | - |