@TechReport{	  it:2018-008,
  author	= {Owe Axelsson and Maya Neytcheva and Anders Str{\"o}m},
  title		= {An Efficient Preconditioning Method for State
		  Box-Constrained Optimal Control Problems},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2018},
  number	= {2018-008},
  month		= mar,
  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.},
  abstract	= {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.}
}