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
Main Authors: Zhang, Xueqing, Peng, Jianwen, Ghosh, Debdas, Yao, Jen-Chih
Format: Journal Article
Language:English
Published: 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.
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
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  surname: Zhang
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  email: zxqcqspb@163.com
  organization: School of International Business and Management, Sichuan International Studies University, Chongqing, 400031, People’s Republic of China
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  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
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  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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Keywords Linearized ADMM
Global convergence
Image compression
Generalized ADMM
Separable convex optimization
Language English
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Snippet The generalized alternating direction method of multipliers (GADMM) has attracted considerable attention due to its versatile applications. This study...
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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
URI https://dx.doi.org/10.1016/j.cam.2024.116483
Volume 462
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