A trust region method for parabolic boundary control problems

In this paper we develop a trust region algorithm for constrained parabolic boundary control problems. For the computation of a trust region step we p ropose an iterative scheme which is a projected form of the Steihaug trust region conjugate gradient method. To ensure the good local convergence prop erties in the terminal phase, a smoothing step at each iteration is added. This step and the projection require the modification of the standard trust region algorithm and its convergence proof. The algorithm has sup-norm con vergence in the terminal phase and L-2 convergence in the global phase. The results are illustrated for a parabolic boundary control problem.