Optimal control problems can be interpreted as optimization problems in function spaces. Here, it is important to exploit the special structure of such problems to, e.g., characterize properties of solutions or develop efficient solution methods.
Non-smooth problems are challenging for analysis and numerics. In particular, the development of optimality conditions is subject of current research.
Another aspect of our research are ill-posed or ill-conditioned optimization problems. We investigate regularization methods to obtain stable numerical approximations.