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MSC: 49K20 65N55 Keywords: Multigrid methods Saddle point system PDE-constrained optimization Control constraints Primal-dual active set methods a b s t r a c t We consider the fast and efficient numerical solution of linear-quadratic optimal control problems with additional constraints on the control. Discretization of the first-order conditions leads to an indefinite linear system of saddle point type with additional complementarity conditions due to the control constraints. Thedoi:10.1016/j.cam.2011.04.002 fatcat:2g6utu646jcozfbrq5b2fpchkq