Uppsala University Department of Information Technology

Technical Report 2018-008

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

Owe Axelsson, Maya Neytcheva, and Anders Ström

March 2018

An efficient preconditioning technique used earlier for two-by-two block matrix systems with square matrix blocks 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 occur 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.

Note: This is a major revision of Technical Report 2017-004. In the new version all the numerical experiments have been rerun with new much more efficient dynamic stopping criteria.

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