A three-block linearized generalized ADMM based iterative algorithm for separable convex programming with application to an image compression problem
The generalized alternating direction method of multipliers (GADMM) has attracted considerable attention due to its versatile applications. This study introduces an innovative adaptation called the linearized GADMM (L-GADMM), which is specifically tailored for solving convex optimization problems. T...
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| Published in: | Journal of computational and applied mathematics Vol. 462; p. 116483 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.07.2025
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| ISSN: | 0377-0427 |
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| Abstract | The generalized alternating direction method of multipliers (GADMM) has attracted considerable attention due to its versatile applications. This study introduces an innovative adaptation called the linearized GADMM (L-GADMM), which is specifically tailored for solving convex optimization problems. The objective function of the problems under consideration encompasses three distinct convex components with no interdependencies among variables or linear constraints. We establish a set of sufficient conditions ensuring the global convergence of the proposed L-GADMM technique for the three-block separable convex minimization problem. Moreover, a series of numerical experiments are conducted to showcase the effectiveness of L-GADMM in tasks such as image compression and calibration of correlation matrices. |
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| AbstractList | The generalized alternating direction method of multipliers (GADMM) has attracted considerable attention due to its versatile applications. This study introduces an innovative adaptation called the linearized GADMM (L-GADMM), which is specifically tailored for solving convex optimization problems. The objective function of the problems under consideration encompasses three distinct convex components with no interdependencies among variables or linear constraints. We establish a set of sufficient conditions ensuring the global convergence of the proposed L-GADMM technique for the three-block separable convex minimization problem. Moreover, a series of numerical experiments are conducted to showcase the effectiveness of L-GADMM in tasks such as image compression and calibration of correlation matrices. |
| ArticleNumber | 116483 |
| Author | Peng, Jianwen Ghosh, Debdas Zhang, Xueqing Yao, Jen-Chih |
| Author_xml | – sequence: 1 givenname: Xueqing surname: Zhang fullname: Zhang, Xueqing email: zxqcqspb@163.com organization: School of International Business and Management, Sichuan International Studies University, Chongqing, 400031, People’s Republic of China – sequence: 2 givenname: Jianwen surname: Peng fullname: Peng, Jianwen email: jwpeng168@hotmail.com organization: School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, People’s Republic of China – sequence: 3 givenname: Debdas surname: Ghosh fullname: Ghosh, Debdas email: debdas.mat@iitbhu.ac.in organization: Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, 221005, India – sequence: 4 givenname: Jen-Chih surname: Yao fullname: Yao, Jen-Chih email: yaojc@mail.cmu.edu.tw organization: Academy of Romanian Scientists, Bucharest, 50044, Romania |
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| Cites_doi | 10.1137/110836936 10.1016/0898-1221(76)90003-1 10.1016/j.cam.2019.02.028 10.1090/S0025-5718-2012-02598-1 10.1137/110822347 10.1007/s40305-015-0084-0 10.1007/s11425-016-9184-4 10.1007/s11590-019-01473-2 10.1142/S0217595915500244 10.1007/s10589-016-9860-y 10.1007/s10898-018-0697-z 10.1007/s11590-023-02063-z 10.1137/0716071 10.1016/j.apnum.2020.09.016 10.1007/BF00927673 10.1007/s11425-013-4683-0 10.1016/j.cam.2021.113503 10.1016/S0168-2024(08)70034-1 10.1561/2200000016 10.1007/BF01581204 10.1007/BF02196592 10.1007/s10107-014-0826-5 10.1007/s10589-012-9510-y 10.1109/ICEDIF.2015.7280231 10.1016/S0167-6377(98)00044-3 10.1007/s11075-022-01491-9 10.1007/s10589-018-9994-1 10.1007/s12532-015-0078-2 10.1007/s11590-023-01997-8 10.1137/110833543 |
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| Keywords | Linearized ADMM Global convergence Image compression Generalized ADMM Separable convex optimization |
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| SubjectTerms | Generalized ADMM Global convergence Image compression Linearized ADMM Separable convex optimization |
| Title | A three-block linearized generalized ADMM based iterative algorithm for separable convex programming with application to an image compression problem |
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