  PDE-constrained optimization problems with control or state constraints are
challenging from an analytical as well as numerical perspective. The
combination of these constraints with a sparsity-promoting $\rm L^1$ term
within the objective function requires sophisticated optimization methods. We
propose the use of an Interior Point scheme applied to a smoothed reformulation
of the discretized problem, and illustrate that such a scheme exhibits robust
performance with respect to parameter changes. To increase the potency of this
method we introduce fast and efficient preconditioners which enable us to solve
problems from a number of PDE applications in low iteration numbers and CPU
times, even when the parameters involved are altered dramatically.
