(Discrete) mathematical optimization with multiple players

Proposed for the academic years 2026-2028

• Robust and bilevel optimization are two powerful paradigms in mathematical programming that address different types of decision-making challenges. Robust optimization focuses on protecting solutions against uncertainty in problem data by seeking decisions that remain feasible and effective under all (or most) possible realizations of uncertain parameters. Bilevel optimization, on the other hand, models hierarchical decision processes involving a leader and a follower, where the leader’s optimal choice depends on the rational response of the follower. This lecture will introduce the basic modelling and solution concepts of these two closely related frameworks. It will start with introducing basic principles of (mixed-integer) linear programming. It will cover theoretical aspects (reformulations, complexity) as well as algorithmic approaches, insisting on the numerical efficiency of the proposed approaches.