Martin Schmidt It is common opinion that generalized Nash equilibrium problems are harder than Nash equilibrium problems. In this work, we show that by adding a new player, it is possible to reduce many generalized problems to standard equilibrium problems. The reduction holds for linear problems and smooth convex problems verifying a Slater-type condition. We also derive … Read more
We consider combinatorial multi-item markets and propose the notion of a ∆-regret Walras equilibrium, consisting of an allocation and item prices such that prices clear the market, the allocation is capacity-feasible, and the players’ strategies lead to a total regret of at most ∆. Regret is the sum of the players’ utility gaps relative to … Read more
Generalized Nash equilibrium problems with mixed-integer variables constitute an important class of games in which each player solves a mixed-integer optimization problem, where both the objective and the feasible set is parameterized by the rivals’ strategies. However, such games are known for failing to admit exact equilibria and also the assumption of all players being … Read more
We present a new difference of convex functions algorithm (DCA) for solving linear and nonlinear mixed complementarity problems (MCPs). The approach is based on the reformulation of bilinear complementarity constraints as difference of convex (DC) functions, more specifically, the difference of scalar, convex quadratic terms. This reformulation gives rise to a DC program, which is … Read more
Bilevel optimization problems arise in numerous real-world applications. While single-level reformulations are a common strategy for solving convex bilevel problems, such approaches usually fail when the follower’s problem includes integer variables. In this paper, we present the first single-level reformulation for mixed-integer linear bilevel optimization, which does not rely on the follower’s value function. Our … Read more
We consider Nash equilibrium problems with mixed-integer variables in which each player solves a mixed-integer optimization problem parameterized in the rivals’ strategies. We distinguish between standard Nash equilibrium problems (NEP), where the parameterization acts only on the players’ cost functions and generalized Nash equilibrium problems (GNEPs), where, additionally, the strategy spaces of the players may … Read more
We consider mixed-integer linear chance-constrained problems for which the random vector that parameterizes the feasible region has finite support. Our key objective is to improve branch-and-bound or -cut approaches by introducing new types of valid inequalities that improve the dual bound and, by this, the overall performance of such methods. We introduce so-called multi-disjunctive valid … Read more
The literature on pessimistic linear 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 … 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 provides an extensive computational study for … Read more
In recent years, significant attention has been devoted to the issue of explainability in automated decision-making tools. The idea is to explain the outcome of a model by presenting a certain change in the input of the model so that the outcome changes significantly. In this paper, we study this question for linear optimization problems … Read more