Constraint-Preconditioned Krylov Solvers for Regularized Saddle-Point Systems

We consider the iterative solution of regularized saddle-point systems. When leading block is symmetric and positive semidefinite on an appropriate subspace, Dollar et al. [SIAM J. Matrix Anal. Appl., 28 (2006), pp. 170--189] describe how to apply conjugate gradient (CG) method coupled with a constraint preconditioner, choice that has proved be effective in optimization applications. investigate design constraint-preconditioned variants other Krylov methods for systems by focusing underlying basis-generation process. build upon principles laid out Gould, Orban, Rees 35 (2014), 1329--1343] provide general guidelines allow us specialize any In particular, we obtain Lanczos Arnoldi-based methods, including version CG, MINRES, SYMMLQ, GMRES($\ell$), DQGMRES. also MATLAB implementations hopes they are useful as basis development more sophisticated software. Finally, illustrate numerical behavior solvers using nonsymmetric arising from constrained optimization.