The research group Mathematical Optimization Methods complements the application-specific projects of the Department Optimization by developing and implementing algorithms for abstract classes of mathematical optimization problems. Our main focus are methods from integer programming, which allows to model and optimize over yes/no decisions and indivisible goods under constrained resources.  Our prime interest lies in algorithms that provide proven guarantees on the solution quality even for highly complex problems for which globally optimal solutions are difficult to compute within time limitations relevant in practice.

Countless applications from traffic, logistics, telecommunications, energy, biochemistry, and many other areas can be formulated as so-called mixed-integer linear or nonlinear programs, in short MIPs or MINLPs, respectively. This versatility, however, keeps posing computational challenges to generic solution approaches and motivates the continuing development of the existing solution techniques.

To a large extent the results of our research contribute to the improvement of the SCIP Optimization Suite: a collection of software packages that is freely available for academic research purposes and available in source code. In the framework of the Research Campus MODAL we collaborate with industrial users of optimization solutions and leading development teams of optimization software for MIP and MINLP.