The professorship conducts research in the field of mixed-integer linear and nonlinear numerical optimization. To solve optimization problems, exact methods are used which, in addition to feasible solutions, provide an certificate of their quality and, ideally, provide a proof of global optimality. In addition, heuristic procedures are used. Where established methods fail, they are adjusted and improved to increase the range of their applications. In cooperation with partners from industry, economy and science, current optimization questions are identified and formulated as algebraic models.