Spring School on " MINLPs and Bilevel Problems"

Tuesday, 22 June, 2021 to Wednesday, 23 June, 2021

Martin Schmidt and Yasmine Beck
Trier University - Department of Mathematics, Germany

Registrations are closed.
To see the list of registered participants, click here

The lectures have been given via video conference (the video can be found below)


his two-day spring school consists of the two parts
- Introduction to MINLP,
- Introduction to Bilevel MI(N)LP.

Both parts will take a one day each.

In the first part, we discuss the class of mixed-integer nonlinear optimization problems (MINLPs). You will learn what an MINLP is, how to distinguish between convex and nonconvex MINLPs, and how to apply standard MINLP modeling techniques. Moreover, you will learn about and understand the classic algorithms for MINLP such as nonlinear branch-and-bound or outer approximation for convex MINLPs as well as the basics of relaxation strategies and spatial branch-and-bound for nonconvex MINLPs.

The second part introduces the class of bilevel optimization problems. We will discuss some exemplary applications and study academic examples that highlight the many difficulties of bilevel optimization. These examples are also used to introduce different solution concepts of bilevel optimization such as optimistic and pessimistic solutions. Afterward, we discuss different single-level reformulation techniques for bilevel problems with convex lower-level problems, before we discuss classic branch-and-bound as well as branch-and-cut techniques for bilevel problems including integer variables. In the end, we will give an outlook over the field of mixed-integer nonlinear bilevel problems.


Slides of both days and lecture notes of Martin Shmidt


Schedule and videos

Introduction to MINLP (Tuesday, June 22, 2021):
 9:00-10:30 MINLP Part 1  See the video
            Short break
11:00-12:30 MINLP Part 2 See the video
            Lunch break
14:00-15:30 MINLP Part 3 See the video
            Short break
16:15-17:45 MINLP exercises (in groups/breakout sessions)
18:00-19:00 "After School" with gather.tow
Introduction to bilevel MI(N)LP (Wednesday, June 23, 2021):
 9:00-10:30 Bilevel Optimization Part 1 See the video
            Short break
11:00-12:30 Bilevel Optimization Part 2 See the video
            Lunch break
14:00-15:30 Bilevel Optimization Part 3 See the video
            Short break
16:15-17:45 Bilevel Optimization exercises (in groups/breakout sessions)

18:00-19:00 "After School" with gather.town


Exercise class

Besides the classic lectures on these topics we will also have an exercise class on both days. In these exercise classes you will also need to model and implement some MINLP and bilevel problems. To be prepared for this please check that you have the following list of software packages installed and tested on your machine.
The idea is that you can directly start to work on the exercises on these days and that you do not have to spend some time during these two days for installing software. You will need:
If possible, always go for the latest versions.