A topological derivative-based algorithm to solve optimal control problems with \(L^0(\Omega)\) control cost (Q6567235)

The paper derives a novel descent method for PDE-constrained optimal control problems that involve the \(L^0\)-cost of the control, i.e., the measure of the support of the control. A fundamental tool is the topological derivative of the value function with respect to variations of the support. For instance, it is shown that the pointwise a.e. non-negativity of this topological derivative is a necessary optimality condition, and the construction of the descent direction is based on this derivative. As main result it is proved that the algorithm generates a minimizing sequence for the value function. Interesting numerical examples like a binary control problem are also included.