Generalized Augmented Lagrangian-SOR Iteration Method for Saddle-Point Systems Arising from Distributed Control Problems
Year: 2016
Author: Min-Li Zeng, Guo-Feng Zhang, Zhong Zheng
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1511-m2015-0297
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 2 : pp. 174–185
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: PDE-constraint optimization Saddle-point matrices Augmented Lagrangian method Convergence Preconditioning.