An Efficient Preconditioning Method for State Box-Constrained Optimal Control Problems

• An efficient preconditioning technique used earlier for two-by-two block matrix systems with square matrices is shown to be applicable also for a state variable box-constrained optimal control problem. The problem is penalized by a standard regularization term for the control variable and for the box-constraint, using a Moreau-Yosida penalization method. It is shown that there arises very few nonlinear iteration steps and also few iterations to solve the arising linearized equations on the fine mesh. This holds for a wide range of the penalization and discretization parameters. The arising nonlinearity can be handled with a hybrid nonlinear-linear procedure that raises the computational efficiency of the overall solution method.

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