The 24th edition of the Belgian Mathematical Optimization Workshop will finally take place on the **22nd and 23rd of April 2024**. It will be held at the Floréal Club, avenue de Villez, 6, 6980 La Roche-en-Ardennes.

This year's edition is supported by ORBEL.

LIMOS, Université Clermont Auvergne, France

**Quantum Computing for Operations Research** (joint work with **Gérard Fleury**)

In this presentation, we aim to provide a concise overview of Quantum Computing, specifically focusing on optimization. Initially, we will present a quick panorama, followed by an initial understanding of qubits, quantum gates, resulting circuits to create the first algorithms. Secondly, from a more practical standpoint, we will discuss funding from the quantum plan and initiatives that have commenced within the Operations Research community. We will present a few historical algorithms, notably Grover's algorithm, which enables searching for an element in an array without having to traverse the entire array, and we will show how it is capable of solving problems such as SAT. We will conclude with an introduction to quantum metaheuristics, providing some examples of their application to Operations Research problems, specifically focusing on the Traveling Salesman Problem (TSP) and graph coloring. Finally, we will wrap up by identifying the upcoming challenges and implications of quantum computing for Operations Research in the years to come.

Department of Mathematics, Trier University, Germany

**A Gentle and Incomplete Introduction to Bilevel Optimization**

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 computational bilevel optimization increased a lot over the last decade and is still growing. Independent of whether the bilevel problem itself contains integer variables or not, many state-of-the-art solution approaches for bilevel optimization make use of techniques that originate from mixed-integer programming. These techniques include branch-and-bound methods, cutting planes and, thus, branch-and-cut approaches, or problem-specific decomposition methods. In this tutorial, we discuss bilevel-tailored approaches that exploit mixed-integer programming techniques to solve bilevel optimization problems. To this end, we first consider bilevel problems with convex or, in particular, linear lower-level problems. The discussed solution methods in this field stem from original works from the 1980's but, on the other hand, are still actively researched today. Moreover, we review modern algorithmic approaches to solve mixed-integer bilevel problems that contain integrality constraints in the lower level.

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**Contact: **Bernard Fortz