The talk summarizes our results obtained when studying the possible application of innovative integrators (operator splitting  procedures and exponential integrators) to optimal control problems. We introduce the innovative integrators considered, and present the advantages and drawbacks of their use. After introducing the abstract optimal control problem having a linear quadratic cost function, we prove the convergence of innovative integrators applied to it. To do so, we briefly summarize the main results in operator semigroup theory, used in the proof. As an example, we treat the linear quadratic regulator problem of the one-dimensional and two-dimensional shallow water equations, and illustrate our results by numerical experiments.

The results are based on the joint works with Johannes Winckler (Tübingen) and Hermann Mena (Innsbruck).