Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor exploited computationally. Based on the recent results by Goerigk et al. (2025), this paper is the first one that reformulates a given strictly robust optimization … Read more
Optimization problems involving equilibrium constraints capture diverse optimization settings such as bi-level optimization, min-max problems and games, and the minimization over non-linear constraints. This paper introduces an Augmented Lagrangian approach with Hessian-vector product approximation to address an equilibrium constrained nonconvex nonsmooth optimization problem. The underlying model in particular captures various settings of bi-level optimization problems, … Read more
Binary bilevel programs are notoriously difficult to solve due to the absence of strong and efficiently computable relaxations. In this work, we introduce a novel single-level reformulation of these programs by leveraging a network flow-based representation of the follower’s value function, utilizing decision diagrams and linear programming duality. This approach enables the development of scalable … Read more
This study addresses discrete network design problems under traffic equilibrium conditions or DNDPs. Given a network and a budget, DNDPs aim to model all-or-nothing decisions such as link addition to minimize network congestion effects. Congestion is measured using traffic equilibrium theory where link travel times are modeled as convex flow-dependent functions and where users make … Read more
Bilevel optimization has garnered growing interest over the past decade. However, little attention has been paid to detecting and dealing with unboundedness in these problems, with most research assuming a bounded high-point relaxation. In this paper, we address unboundedness in bilevel and multilevel optimization by studying its computational complexity. We show that deciding whether an … Read more
In this report, we present the BOBILib, a collection of more than 2600 instances of mixed integer bilevel linear optimization problems (MIBLPs). The goal of this library is to provide a large and well-curated set of test instances freely available for the research community so that new and existing algorithms in bilevel optimization can be … Read more
We present a branch-and-cut method for solving convex integer nonlinear bilevel problems, i.e., bilevel models with nonlinear but jointly convex objective functions and constraints in both the upper and the lower level. To this end, we generalize the idea of using disjunctive cuts to cut off integer-feasible but bilevel-infeasible points. These cuts can be obtained … Read more