Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem
We consider the problem of seeking a symmetric positive semidefinite matrix in a closed convex set to approximate a given matrix. This problem may arise in several areas of numerical linear algebra or come from finance industry or statistics and thus has many applications. For solving this class of...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/598563 |
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| author | Minghua Xu Yong Zhang Qinglong Huang Zhenhua Yang |
| author_facet | Minghua Xu Yong Zhang Qinglong Huang Zhenhua Yang |
| author_sort | Minghua Xu |
| collection | DOAJ |
| description | We consider the problem of seeking a symmetric positive semidefinite matrix in a closed convex set to approximate a given matrix. This problem may arise in several areas of numerical linear algebra or come from finance industry or statistics and thus has many applications. For solving this class of matrix optimization problems, many methods have been proposed in the literature. The proximal alternating direction method is one of those methods which can be easily applied to solve these matrix optimization problems. Generally, the proximal parameters of the proximal alternating direction method are greater than zero. In this paper, we conclude that the restriction on the proximal parameters can be relaxed for solving this kind of matrix optimization problems. Numerical experiments also show that the proximal alternating direction method with the relaxed proximal parameters is convergent and generally has a better performance than the classical proximal alternating direction method. |
| format | Article |
| id | doaj-art-d263592cfba44be09e2d4310f146a45a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d263592cfba44be09e2d4310f146a45a2025-02-03T05:57:53ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/598563598563Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment ProblemMinghua Xu0Yong Zhang1Qinglong Huang2Zhenhua Yang3School of Mathematics and Physics, Changzhou University, Jiangsu 213164, ChinaSchool of Mathematics and Physics, Changzhou University, Jiangsu 213164, ChinaSchool of Mathematics and Physics, Changzhou University, Jiangsu 213164, ChinaCollege of Science, Nanjing University of Posts and Telecommunications, Jiangsu 210003, ChinaWe consider the problem of seeking a symmetric positive semidefinite matrix in a closed convex set to approximate a given matrix. This problem may arise in several areas of numerical linear algebra or come from finance industry or statistics and thus has many applications. For solving this class of matrix optimization problems, many methods have been proposed in the literature. The proximal alternating direction method is one of those methods which can be easily applied to solve these matrix optimization problems. Generally, the proximal parameters of the proximal alternating direction method are greater than zero. In this paper, we conclude that the restriction on the proximal parameters can be relaxed for solving this kind of matrix optimization problems. Numerical experiments also show that the proximal alternating direction method with the relaxed proximal parameters is convergent and generally has a better performance than the classical proximal alternating direction method.http://dx.doi.org/10.1155/2014/598563 |
| spellingShingle | Minghua Xu Yong Zhang Qinglong Huang Zhenhua Yang Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem Abstract and Applied Analysis |
| title | Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem |
| title_full | Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem |
| title_fullStr | Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem |
| title_full_unstemmed | Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem |
| title_short | Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem |
| title_sort | proximal alternating direction method with relaxed proximal parameters for the least squares covariance adjustment problem |
| url | http://dx.doi.org/10.1155/2014/598563 |
| work_keys_str_mv | AT minghuaxu proximalalternatingdirectionmethodwithrelaxedproximalparametersfortheleastsquarescovarianceadjustmentproblem AT yongzhang proximalalternatingdirectionmethodwithrelaxedproximalparametersfortheleastsquarescovarianceadjustmentproblem AT qinglonghuang proximalalternatingdirectionmethodwithrelaxedproximalparametersfortheleastsquarescovarianceadjustmentproblem AT zhenhuayang proximalalternatingdirectionmethodwithrelaxedproximalparametersfortheleastsquarescovarianceadjustmentproblem |