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We address the problem of preconditioning a sequence of saddle point linearsystems arising in the solution of PDE-constrained optimal control problems viaactive-set Newton methods, with control and (regularized) state constraints. Wepresent two new preconditioners based on a full block matrix factorization ofthe Schur complement of the Jacobian matrices, where the active-set blocks aremerged into the constraint blocks. We discuss the robustness of the newpreconditioners with respect to the parameters of the continuous and discreteproblems. Numerical experiments on 3D problems are presented, includingcomparisons with existing approaches based on preconditioned conjugategradients in a nonstandard inner product.

Preconditioning of Active-Set Newton Methods for PDE-constrained Optimal Control Problems