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Volume 34, Issue 2
Generalized Augmented Lagrangian-SOR Iteration Method for Saddle-Point Systems Arising from Distributed Control Problems

Min-Li Zeng, Guo-Feng Zhang & Zhong Zheng

DOI: 10.4208/jcm.1511-m2015-0297

J. Comp. Math., 34 (2016), pp. 174-185.

Published online: 2016-04

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  • Abstract

In this paper, a generalized augmented Lagrangian-successive over-relaxation (GAL-SOR) iteration method is presented for solving saddle-point systems arising from distributed control problems. The convergence properties of the GAL-SOR method are studied in detail. Moreover, when 0 ‹ ω ‹ 1 and Q = $\frac{1}{γ}I$, the spectral properties for the preconditioned matrix are analyzed. Numerical experiments show that if the mass matrix from the distributed control problems is not easy to inverse and the regularization parameter β is very small, the GAL-SOR iteration method can work well.

  • Keywords

PDE-constraint optimization, Saddle-point matrices, Augmented Lagrangian method, Convergence, Preconditioning.

  • AMS Subject Headings

65F10, 65F50.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zengml12@lzu.edu.cn (Min-Li Zeng)

gf_zhang@lzu.edu.cn (Guo-Feng Zhang)

zhengzh13@lzu.edu.cn (Zhong Zheng)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-174, author = {Zeng , Min-LiZhang , Guo-Feng and Zheng , Zhong}, title = {Generalized Augmented Lagrangian-SOR Iteration Method for Saddle-Point Systems Arising from Distributed Control Problems}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {2}, pages = {174--185}, abstract = {

In this paper, a generalized augmented Lagrangian-successive over-relaxation (GAL-SOR) iteration method is presented for solving saddle-point systems arising from distributed control problems. The convergence properties of the GAL-SOR method are studied in detail. Moreover, when 0 ‹ ω ‹ 1 and Q = $\frac{1}{γ}I$, the spectral properties for the preconditioned matrix are analyzed. Numerical experiments show that if the mass matrix from the distributed control problems is not easy to inverse and the regularization parameter β is very small, the GAL-SOR iteration method can work well.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1511-m2015-0297}, url = {http://global-sci.org/intro/article_detail/jcm/9789.html} }
TY - JOUR T1 - Generalized Augmented Lagrangian-SOR Iteration Method for Saddle-Point Systems Arising from Distributed Control Problems AU - Zeng , Min-Li AU - Zhang , Guo-Feng AU - Zheng , Zhong JO - Journal of Computational Mathematics VL - 2 SP - 174 EP - 185 PY - 2016 DA - 2016/04 SN - 34 DO - http://doi.org/10.4208/jcm.1511-m2015-0297 UR - https://global-sci.org/intro/article_detail/jcm/9789.html KW - PDE-constraint optimization, Saddle-point matrices, Augmented Lagrangian method, Convergence, Preconditioning. AB -

In this paper, a generalized augmented Lagrangian-successive over-relaxation (GAL-SOR) iteration method is presented for solving saddle-point systems arising from distributed control problems. The convergence properties of the GAL-SOR method are studied in detail. Moreover, when 0 ‹ ω ‹ 1 and Q = $\frac{1}{γ}I$, the spectral properties for the preconditioned matrix are analyzed. Numerical experiments show that if the mass matrix from the distributed control problems is not easy to inverse and the regularization parameter β is very small, the GAL-SOR iteration method can work well.

Zeng , Min-LiZhang , Guo-Feng and Zheng , Zhong. (2016). Generalized Augmented Lagrangian-SOR Iteration Method for Saddle-Point Systems Arising from Distributed Control Problems. Journal of Computational Mathematics. 34 (2). 174-185. doi:10.4208/jcm.1511-m2015-0297
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