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Volume 42, Issue 6
Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing

Jianchao Bai, Ke Guo, Junli Liang, Yang Jing & H.C. So

DOI: 10.4208/jcm.2305-m2021-0107

J. Comp. Math., 42 (2024), pp. 1605-1626.

Published online: 2024-11

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  • Abstract

The alternating direction method of multipliers (ADMM) has been extensively investigated in the past decades for solving separable convex optimization problems, and surprisingly, it also performs efficiently for nonconvex programs. In this paper, we propose a symmetric ADMM based on acceleration techniques for a family of potentially nonsmooth and nonconvex programming problems with equality constraints, where the dual variables are updated twice with different stepsizes. Under proper assumptions instead of the so-called Kurdyka-Lojasiewicz inequality, convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals, respectively. Performance of our algorithm is verified by numerical examples corresponding to signal processing applications in sparse nonconvex/convex regularized minimization.

  • Keywords

Nonconvex optimization, Symmetric ADMM, Acceleration technique, Complexity, Signal processing.

  • AMS Subject Headings

47A30, 65Y20, 90C26, 90C90

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-1605, author = {Bai , JianchaoGuo , KeLiang , JunliJing , Yang and So , H.C.}, title = {Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {6}, pages = {1605--1626}, abstract = {

The alternating direction method of multipliers (ADMM) has been extensively investigated in the past decades for solving separable convex optimization problems, and surprisingly, it also performs efficiently for nonconvex programs. In this paper, we propose a symmetric ADMM based on acceleration techniques for a family of potentially nonsmooth and nonconvex programming problems with equality constraints, where the dual variables are updated twice with different stepsizes. Under proper assumptions instead of the so-called Kurdyka-Lojasiewicz inequality, convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals, respectively. Performance of our algorithm is verified by numerical examples corresponding to signal processing applications in sparse nonconvex/convex regularized minimization.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2305-m2021-0107}, url = {http://global-sci.org/intro/article_detail/jcm/23509.html} }
TY - JOUR T1 - Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing AU - Bai , Jianchao AU - Guo , Ke AU - Liang , Junli AU - Jing , Yang AU - So , H.C. JO - Journal of Computational Mathematics VL - 6 SP - 1605 EP - 1626 PY - 2024 DA - 2024/11 SN - 42 DO - http://doi.org/10.4208/jcm.2305-m2021-0107 UR - https://global-sci.org/intro/article_detail/jcm/23509.html KW - Nonconvex optimization, Symmetric ADMM, Acceleration technique, Complexity, Signal processing. AB -

The alternating direction method of multipliers (ADMM) has been extensively investigated in the past decades for solving separable convex optimization problems, and surprisingly, it also performs efficiently for nonconvex programs. In this paper, we propose a symmetric ADMM based on acceleration techniques for a family of potentially nonsmooth and nonconvex programming problems with equality constraints, where the dual variables are updated twice with different stepsizes. Under proper assumptions instead of the so-called Kurdyka-Lojasiewicz inequality, convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals, respectively. Performance of our algorithm is verified by numerical examples corresponding to signal processing applications in sparse nonconvex/convex regularized minimization.

Bai , JianchaoGuo , KeLiang , JunliJing , Yang and So , H.C.. (2024). Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing. Journal of Computational Mathematics. 42 (6). 1605-1626. doi:10.4208/jcm.2305-m2021-0107
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