A topological derivative-based algorithm to solve optimal control problems with $L^0(Ω)$ control cost

Daniel Wachsmuth

Published 2022-11-22Version 1

In this paper, we consider optimization problems with $L^0$-cost of the controls. Here, we take the support of the control as independent optimization variable. Topological derivatives of the corresponding value function with respect to variations of the support are derived. These topological derivatives are used in a novel algorithm. In the algorithm, topology changes happen at large values of the topological derivative. Convergence results are given.