Mathematics

Parametric optimal control problems are an important class of problems studied because of their applicability to many real models in many different research areas. Hence, one could be interested in being able to numerically solve this kind of problems efficiently. To this aim, this work wants to investigate two different computational reduction strategies, i.e., the hierarchical model reduction method (Hi-Mod) and the reduced basis method (RB). First of all, we separately study their applicability to parametrized optimal control problems and we also present some numerical test cases. In particular, we analyze the well-posedness of the saddle-point formulation of an optimal control problem that has been hierarchically reduced. Then, we propose a possible way to combine the two methods mentioned above. We validate this new procedure on some selected numerical benchmarks.