Martin Schmidt

On Multidimensonal Disjunctive Inequalities for Chance-Constrained Stochastic Problems with Finite Support

  • Diego Cattaruzza
  • Martine Labbé
  • Matteo Petris
  • Marius Roland
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    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 bounds and, by this, the overall performance of such methods. We introduce so-called primal-dual as … Read more

    On Coupling Constraints in Pessimistic Linear Bilevel Optimization

  • Dorothee Henke
  • Henri Lefebvre
  • Martin Schmidt
  • Johannes Thürauf
    • Categories Bilevel Optimization Tags , , ,

    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

    A Computational Study for Solving Decision-Dependent Robust Problems as Bilevel Optimization Problems

  • Henri Lefebvre
  • Martin Schmidt
  • Simon Stevens
  • Johannes Thürauf
    • Categories Bilevel Optimization, Robust Optimization Tags , , ,

    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

    Computing Weak Counterfactual Explanations for Linear Optimization: A New Class of Bilevel Models and a Tailored Penalty Alternating Direction Method

  • Henri Lefebvre
  • Martin Schmidt
    • Categories Energy, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

    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

    Mixed-Integer Bilevel Optimization with Nonconvex Quadratic Lower-Level Problems: Complexity and a Solution Method

  • Immanuel M. Bomze
  • Martin Schmidt
  • Horländer Andreas
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , ,

    We study bilevel problems with a convex quadratic mixed-integer upper-level, integer linking variables, and a nonconvex quadratic, purely continuous lower-level problem. We prove $\Sigma_p^2$-hardness of this class of problems, derive an iterative lower- and upper-bounding scheme, and show its finiteness and correctness in the sense that it computes globally optimal points or proves infeasibility of … Read more

    Computational Methods for the Household Assignment Problem

  • Ulf Friedrich
  • Lucas Moschen
  • Ralf Münnich
  • Martin Schmidt
    • Categories Applications - OR and Management Sciences, Approximation Algorithms, Integer Programming Tags , , , ,

    We consider the problem of assigning the entries of a household data set to real-world address data. This household assignment problem occurs in the geo-referencing step of spatial microsimulation models. The resulting combinatorial optimization model is a maximum weight matching problem with additional side constraints. Even for real-world instances of medium size, such as the … Read more

    BOBILib: Bilevel Optimization (Benchmark) Instance Library

  • Johannes Thürauf
  • Thomas Kleinert
  • Ivana Ljubić
  • Ted K. Ralphs
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Bilevel Optimization, Optimization Software Benchmark Tags , , , ,

    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

    Exact Augmented Lagrangian Duality for Nonconvex Mixed-Integer Nonlinear Optimization

  • Henri Lefebvre
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , ,

    In the context of mixed-integer nonlinear problems (MINLPs), it is well-known that strong duality does not hold in general if the standard Lagrangian dual is used. Hence, we consider the augmented Lagrangian dual (ALD), which adds a nonlinear penalty function to the classic Lagrangian function. For this setup, we study conditions under which the ALD … Read more

    Toll Setting with Robust Wardrop Equilibrium Conditions Under Budgeted Uncertainty

  • Yasmine Beck
  • Martine Labbé
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Transportation Tags , , , ,

    We consider two variants of the toll-setting problem in which a traffic authority uses tolls either to maximize revenue or to alleviate bottlenecks in the traffic network. The users of the network are assumed to act according to Wardrop’s user equilibrium so that the overall toll-setting problems are modeled as mathematical problems with equilibrium constraints. … Read more

    Stabilizing GNEP-Based Model Predictive Control: Quasi-GNEPs and End Constraints

  • Falk M. Hante
  • Martin Schmidt
  • Antonia Topalovic
    • Categories Other Topics Tags , , ,

    We present a feedback scheme for non-cooperative dynamic games and investigate its stabilizing properties. The dynamic games are modeled as generalized Nash equilibrium problems (GNEP) in which the shared constraint consists of linear time-discrete dynamic equations (e.g., sampled from a partial or ordinary differential equation), which are jointly controlled by the players’ actions. Further, the … Read more