Model order reduction for a linearized robust PDE constrained optimization

We investigate an optimal control problem governed by a time dependent partial differential equations and due to manufacturing, there are uncertainties which are deterministic in the present work. The resulting optimization problem considers the worst-case scenario over the uncertain domain. The main idea of the method is to linearize the considered cost functional with respect to the uncertain parameters, then to consider the inner maximization of the obtained linear approximation, which can be rewritten as a standard optimization problem. The solution of this problem involves the solution of several PDEs that is computationally expensive, and for this reason, we propose a model reduction approach in order to reduce the complexity of the problem. Numerical results are presented to show the effectiveness of the presented approach.