Generalized Augmented Lagrangian-SOR Iteration Method for Saddle-Point Systems Arising from Distributed Control Problems (Journal of Computational Mathematics, 2018)
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.