In many real-world optimization problems, there is not a single decision-maker, who controls all aspects of the decision process, but there are multiple decision-makers and they often do not have the same goal, but instead have conflicting objectives. Hierarchical optimization problems (HOPs) allow to model such decision-making processes with multiple actors, who act on different levels. A prominent example of such a process is a Stackelberg game, which can be formalized as a bilevel optimization problem (i.e., a HOP with two levels). Due to their power of allowing to model game-theoretic aspects, HOPs have many different application areas, however, they are also very hard to solve, both from a theoretical and also from a practical side.

In this project we want to develop new and extend existing solution algorithms for generic as well as more specific classes of HOPs, such as Mixed-Integer Bilevel Linear problems, Interdiction problems and Fortification problems.