Optimal control problems for the heat equation with pointwise
bilateral control-state constraints are considered. A locally
superlinearly convergent numerical solution algorithm is proposed
and its mesh independence is established. Further, for the
efficient numerical solution reduced space and Schur complement
based preconditioners are proposed which take into account the
active and inactive set structure of the problem. The paper ends
by numerical tests illustrating our theoretical findings and
comparing the efficiency of the proposed preconditioners.