Stefan Takacs successfully defended his thesis - Many congratulations!
In this thesis we construct and analyze multigrid methods for solving the optimality system characterizing the solution of an optimal control problem. Originally multigrid methods were constructed for elliptic problems. However, the optimality system is not elliptic. We make use of the fact that the matrix is a block-matrix with saddle point structure: on the one hand we have two blocks of variables representing state and control. On the other hand, the conversion to the optimality system requires the introduction of Lagrange multipliers, which form the third block of variables. There are several possibilities to use multigrid methods for constructing solvers for such saddle point problems. We apply the multigrid idea directly to the (reduced or not reduced) optimality system, which is called an all-at-once approach. The choice of an appropriate smoother is the key issue in constructing such a multigrid method. In this framework the smoother will be constructed such that the convergence rates are independent of the grid level. For a sub-class of the class of problems we will introduce in a first point, we will go one step further and construct methods where the convergence rates are also robust in a certain regularization or cost parameter which is part of the problem. Moreover, we will show this fact. Methods that do not take this into account typically show quite poor convergence rates if this parameter attains small values.