On Augmented Lagrangian Methods for Saddle-Point Linear Systems with Singular or Semidefinite (1, 1) Blocks (Journal of Computational Mathematics, 2018)
An effective algorithm for solving large saddle-point linear systems, presented by Krukier et al., is applied to the constrained optimization problems. This method is a modification of skew-Hermitian triangular splitting iteration methods. We consider the saddle-point linear systems with singular or semidefinite (1, 1) blocks. Moreover, this method is applied to precondition the GMRES. Numerical results have confirmed the effectiveness of the method and showed that the new method can produce high-quality preconditioners for the Krylov subspace methods for solving large sparse saddle-point linear systems.
Keywords: Hermitian and skew-Hermitian splitting; Saddle-point linear system; Constrained optimization; Krylov subspace method.