EUROPT Summer School 2026

School dates, venue and topics

The school will take place on 6-7 July at the Johannes Kepler Universität Linz, Austria. The school is planned to be in-person only, no live streaming will be provided. There will be two courses focusing on different sides of the continuous optimization world, specifically on

1. Semidefinite programming and iterative optimization algorithms

2. Bilevel optimization

The lectures on semidefinite programming will be delivered by Etienne de Klerk, on bilevel optimization by Martin Schmidt. The two days will included about 6 hours of lectures plus coffee breaks.

Attendance

Attendance is free of charge but with a mandatory registration. Lectures are particularly suited for PhD students and young researchers to provide them with the chance of attending two high level courses on continuous optimization, but the school is open to everyone wishing to participate. To register fill this form by 15 May (please, register only when you are sure you are coming: the available classroom is large, so everyone should have a place – in the very unlikely event of too many registrations the priority will not be set upon early booking).

Timetable

Monday 6 July – Tuesday 7 July

9:00 – 10:30 Lecture I

10:30 – 11:00 Break

11:00 – 12:30 Lecture II

12:30 – 14:00 Lunch break

14:00 – 15:30 Lecture III

15:30 – 16:00 Break

16:00 – 17:30 Lecture IV

The courses

The SemiDefinite Programming approach to analyze the worst-case behavior of iterative optimization methods

by Etienne de Klerk

Computer-assisted proofs are of growing importance in mathematics, with notable success stories like the first proofs of the four-color theorem and Kepler conjecture. A more recent example is the pioneering work by Drori and Teboulle [1], where semidefinite programming is the computational tool.

In this short course, we will review the basic properties of semidefinite programming, as well as the method by Drori and Teboulle. We will also look at more recent developments that enhance the approach, including the work in [2].

Finally, we will look at the worst-case analysis of specific (classical) optimization algorithms, including (stochastic) gradient descent, Newton’s method, and the convex-concave procedure (aka DCA).

As a part of the course, we will experiment with Python and Matlab tools that are available to perform this type of computational analysis, specifically the tools PEPit and PESTO [3], developed by Adrien Taylor and collaborators.

Bibliography and webography

[1] Drori, Y. and Teboulle, M. Performance of first-order methods for smooth convex minimization: a novel approach. Math. Program. 145 (1), 451-482, 2014.

[2] Taylor, A.B., Hendrickx, J.M. and Glineur, F. Smooth strongly convex interpolation and exact worst-case performance of first-order methods. Math. Program. 161, 307–345 (2017).

[3] https://github.com/PerformanceEstimation

A gentle and incomplete introduction to Bilevel Optimization … and some new results

by Martin Schmidt

Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution of another optimization problem. As a consequence, bilevel optimization is able to model hierarchical decision making processes. This is appealing for modeling real-world problems, but it also makes the resulting optimization models hard to solve in theory and practice. The scientific interest in bilevel optimization increased a lot over the last decade and is still growing.

In this tutorial, we discuss the most important aspects that render bilevel problems more challenging than single-level optimization problems and present the basic existence and hardness theory as well as the geometrical properties for linear bilevel models as well as the basic techniques for solving them. After these basics, we will also discuss some exemplary recent contributions in the field that are mainly about the effect of having coupling constraints or not.

The lecturers

Etienne de Klerk (Universiteit van Tilburg)

Etienne de Klerk completed his BSc and MSc degrees at the University of Pretoria in South Africa and obtained his PhD degree from the Delft University of Technology in the Netherlands in 1997. From January 1998 to September 2003, he held assistant professorships at the Delft University of Technology, and from September 2003 to September 2005 an associate professorship at the University of Waterloo, Canada, in the Department of Combinatorics & Optimization. In September 2004 he was appointed at Tilburg University, The Netherlands, first as an associate professor, and then as full professor (from June 2009). From August 29th, 2012, until August 31st, 2013, he was also appointed as full professor in the Division of Mathematics of the School of Physical and Mathematical Sciences at the Nanyang Technological University in Singapore. From September 1st, 2015, to August 31st, 2019, he also held a full professorship at the Delft University of Technology (1 day/week position). Dr. De Klerk’s main research interest is mathematical optimization, and his publications include the monograph Aspects of Semidefinite Programming (Kluwer/Springer, 2002). He has served five 3-year terms as associate editor of the SIAM Journal on Optimization, two 3-year terms as associate editor of the INFORMS Journal Operations Research, and has been guest editor of two issues of Mathematical Programming B.

He is a co-recipient of the Canadian Foundation for Innovation’s New Opportunities Fund award, recipient of the VIDI grant of the Dutch Organization for Scientific Research (NWO), and a co-recipient of the ENW-GROOT grant of the NWO. He received the 2017 Best Paper Prize from the Springer journal Optimization Letters for joint work on the complexity of gradient descent methods. He has been elected EUROPT Fellow in 2026.

Martin Schmidt (Universität Trier)

Martin Schmidt is a Full Professor of Nonlinear Optimization at Trier University and a Fellow of the Energie Campus Nürnberg and SFB Transregio 154. He previously held a junior professorship at Friedrich-Alexander-Universität Erlangen-Nürnberg and received his PhD in Mathematics from Leibniz Universität Hannover. His main research interests are in mixed-integer nonlinear optimization and multilevel optimization, with a particular focus on bilevel optimization. He is actively involved in the mathematical optimization community, regularly giving plenary and keynote talks at international conferences and serving as Associate Editor of the EURO Journal on Computational Optimization and as a member of the Editorial Board of the European Journal of Operational Research. His work has received several international awards, including the EURO Best EJOR Paper Award and the Marguerite Frank Award.