Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing
Year: 2024
Author: Jianchao Bai, Ke Guo, Junli Liang, Yang Jing, H.C. So
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2305-m2021-0107
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1605–1626
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Nonconvex optimization Symmetric ADMM Acceleration technique Complexity Signal processing.
Author Details
Jianchao Bai Email
Ke Guo Email
Junli Liang Email
Yang Jing Email
H.C. So Email
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