Generalized Augmented Lagrangian-SOR Iteration Method for Saddle-Point Systems Arising from Distributed Control Problems

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.

Author Details

Min-Li Zeng

Guo-Feng Zhang

Zhong Zheng