An introduction to quantum optimal control, shape optimization, optical flow and digital inpainting

Alfio Borzi, Universität Würzburg, Germany

In this talk, different optimisation problems are discussed that show the large range of applicability of PDE optimal control techniques. In physics and chemistry, optimal control problems of quantum models is a focus in application, where an optimal control potential is sought that drives the system to attain a given final configuration. In mechanics, shape optimisation problems are considered for the design of structures with optimal mechanical and aerodynamical features. In mathematical imaging, inverse problems are formulated as optimal control problems to efficiently identify objects and their dynamics based on a time-sequence of measurements. Specific classes of these problems are illustrated and solved by numerical optimisation techniques.