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

Authors

  • Min-Li Zeng School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu Province, P.R. China
  • Guo-Feng Zhang School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu Province, P.R. China
  • Zhong Zheng School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, China

DOI:

https://doi.org/10.4208/jcm.1511-m2015-0297

Keywords:

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

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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Published

2018-08-22

Issue

Vol. 34 No. 2 (2016)

Section

Articles