Shape Optimization for Maxwell's Equations Including Hysteresis Effects in the Material Laws

This project aims to develop and analyze an approach for optimizing non-smooth problems in suitable function spaces. The basis for this is initially the globally convergent optimization algorithm LiPsMin, which is tailored to minimize Lipschitz-continuous and piecewise smooth functions. This is extended here to a method for optimization in function spaces. In conjunction with the desired grid independence of the algorithm, this results in a novel alternative to the prevailing semi-smooth Newton methods with their only local convergence behavior.