PRECONDITIONED SOLUTION OF STATE GRADIENT CONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEMS

Elliptic optimal control problems with pointwise state gradient constraints are considered. A quadratic penalty approach is employed together with a semismooth Newton iteration. Three different preconditioners are pro-posed and the ensuing spectral properties of the preconditioned linear New-ton saddle-point systems analyzed in dependence on the penalty parameter. A new bound for the smallest positive eigenvalue is proved. Since the anal-ysis is carried out in function space it will ensure mesh independent conver-gence behavior of suitable Krylov subspace methods such as MINRES also in discretized settings. A path-following strategy with a preconditioned in-exact Newton solver is implemented and numerical results are provided