This talk is concerned with optimizing the spatially variable wave speed in a scalar wave equation whose values are assumed to be taken pointwise from a known finite set. Such a property can be included in optimal control by a so-called ”multibang” penalty that is nonsmooth but convex. Well-posedness as well as the numerical solution of the regularized problem are discussed.
joint work with Günter Leugering, Alexander Martin, Martin Schmidt
We develop a decomposition method in space and time for optimal control problems on networks governed by systems of hyperbolic PDEs. The optimality system of the optimal control problem can be iteratively decomposed such that the resulting subsystems are defined on small time intervals and (possibly) single edges of the network graph. Then, virtual control problems are introduced, which have optimality systems that coincide with the decomposed subsystems. Finally, we prove the convergence of this iterative method to the solution of the original control problem.
joint work with Simone Göttlich, Andreas Potschka, Lars Schewe
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. A lifting allows a decomposition into a mixed-integer optimal control problem without combinatorial constraints and a mixed-integer problem for the combinatorial constraints in the control space. The coupling is handled using a penalty-approach. We present an exactness result for the penalty which yields a solution approach that convergences to partial-epsilon-minima. The quality of these dedicated points can be controlled using the penalty parameter.