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Article: Alternating direction method with Gaussian back substitution for separable convex programming
Title | Alternating direction method with Gaussian back substitution for separable convex programming |
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Authors | |
Keywords | Gaussian back substitution Convex programming Separable structure Alternating direction method |
Issue Date | 2012 |
Publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/siopt.php |
Citation | SIAM Journal on Optimization, 2012, v. 22, n. 2, p. 313-340 How to Cite? |
Abstract | We consider the linearly constrained separable convex minimization problem whose objective function is separable into m individual convex functions with nonoverlapping variables. A Douglas-Rachford alternating direction method of multipliers (ADM) has been well studied in the literature for the special case of m = 2. But the convergence of extending ADM to the general case of m ⥠3 is still open. In this paper, we show that the straightforward extension of ADM is valid for the general case of m ⥠3 if it is combined with a Gaussian back substitution procedure. The resulting ADM with Gaussian back substitution is a novel approach towards the extension of ADM from m = 2 to m ⥠3, and its algorithmic framework is new in the literature. For the ADM with Gaussian back substitution, we prove its convergence via the analytic framework of contractive-type methods, and we show its numerical efficiency by some application problems. © 2012 Society for Industrial and Applied Mathematics. |
Persistent Identifier | http://hdl.handle.net/10722/251004 |
ISSN | 2023 Impact Factor: 2.6 2023 SCImago Journal Rankings: 2.138 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | He, Bingsheng | - |
dc.contributor.author | Tao, Min | - |
dc.contributor.author | Yuan, Xiaoming | - |
dc.date.accessioned | 2018-02-01T01:54:18Z | - |
dc.date.available | 2018-02-01T01:54:18Z | - |
dc.date.issued | 2012 | - |
dc.identifier.citation | SIAM Journal on Optimization, 2012, v. 22, n. 2, p. 313-340 | - |
dc.identifier.issn | 1052-6234 | - |
dc.identifier.uri | http://hdl.handle.net/10722/251004 | - |
dc.description.abstract | We consider the linearly constrained separable convex minimization problem whose objective function is separable into m individual convex functions with nonoverlapping variables. A Douglas-Rachford alternating direction method of multipliers (ADM) has been well studied in the literature for the special case of m = 2. But the convergence of extending ADM to the general case of m ⥠3 is still open. In this paper, we show that the straightforward extension of ADM is valid for the general case of m ⥠3 if it is combined with a Gaussian back substitution procedure. The resulting ADM with Gaussian back substitution is a novel approach towards the extension of ADM from m = 2 to m ⥠3, and its algorithmic framework is new in the literature. For the ADM with Gaussian back substitution, we prove its convergence via the analytic framework of contractive-type methods, and we show its numerical efficiency by some application problems. © 2012 Society for Industrial and Applied Mathematics. | - |
dc.language | eng | - |
dc.publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/siopt.php | - |
dc.relation.ispartof | SIAM Journal on Optimization | - |
dc.subject | Gaussian back substitution | - |
dc.subject | Convex programming | - |
dc.subject | Separable structure | - |
dc.subject | Alternating direction method | - |
dc.title | Alternating direction method with Gaussian back substitution for separable convex programming | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/110822347 | - |
dc.identifier.scopus | eid_2-s2.0-84865692854 | - |
dc.identifier.volume | 22 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 313 | - |
dc.identifier.epage | 340 | - |
dc.identifier.isi | WOS:000306100300003 | - |
dc.identifier.issnl | 1052-6234 | - |