The lecture will give an introduction to Mathematical Programming, in particular LP, ILP, MIP, MINLP. Especially MIP (Mixed Integer Programming) is a very powerful model to solve real-world problems. Even though only linear constraints can be used and the resulting optimisation problems are usually NP-hard, MIP works very well in practice, both in its ability to represent the essential problem structure as well as being practically solvable.
In the beginning, we will show some examples how to model particular structures as they typically appear in industrial models as an Integer Optimisation Problem. In the second part, we give an overview and some particular details on how state-of-the-art branch-and-cut solvers for this class of problems work.