In this paper we propose a sequential minimax optimization (SMO) method for solving a class of constrained bilevel optimization problems in which the lower-level part is a possibly nonsmooth convex optimization problem, while the upper-level part is a possibly nonconvex optimization problem. Specifically, SMO applies a first-order method to solve a sequence of minimax subproblems, … Read more
We consider the central role of improving directions in solution methods for mixed integer bilevel linear optimization problems (MIBLPs). Current state-of-the-art methods for solving MIBLPs employ the branch-and-cut framework originally developed for solving mixed integer linear optimization problems. This approach relies on oracles for two kinds of subproblems: those for checking whether a candidate pair … Read more
In this paper, we investigate the partial inverse knapsack problem, a bilevel optimization problem in which the follower solves a classical 0/1-knapsack problem with item profit values comprised of a fixed part and a modification determined by the leader. Specifically, the leader problem seeks a minimal change to given item profits such that there is … Read more
We study a bilevel optimization framework for hyperparameter learning in variational models, with a focus on sparse regression and classification tasks. In particular, we consider a weighted elastic-net regularizer, where feature-wise regularization parameters are learned through a bilevel formulation. A key novelty of our approach is the use of a Forward-Backward (FB) reformulation of the … Read more
Generalized Nash equilibrium problems with mixed-integer variables form an important class of games in which each player solves a mixed-integer optimization problem with respect to her own variables and the strategy space of each player depends on the strategies chosen by the rival players. In this work, we introduce a branch-and-cut algorithm to compute exact … Read more
With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications are new machine learning formulations that have been proposed in the trilevel context and, as a result, efficient and … Read more
We consider the Mathematical Program with Complementarity Constraints (MPCC). One of the main challenges in solving this problem is the systematic failure of standard Constraint Qualifications (CQs). Carefully accounting for the combinatorial nature of the complementarity constraints, tractable versions of the Mangasarian Fromovitz Constraint Qualification (MFCQ) have been designed and widely studied in the literature. … Read more
The literature on pessimistic bilevel optimization with coupling constraints is rather scarce and it has been common sense that these problems are harder to tackle than pessimistic bilevel problems without coupling constraints. In this note, we show that this is not the case. To this end, given a pessimistic problem with coupling constraints, we derive … Read more
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
We study a bilevel hub location problem where on the upper level, a shipment service provider –the leader–builds a transportation network and sets the prices of shipments on each possible transportation relation. Here, the leader has to take into account the customers’ reaction — the follower — who will only purchase transport services depending on … Read more