linear bilevel optimization

Calmness of the Solution-Set Mapping for Linear Bilevel and Pricing Problems

  • Henri Lefebvre
  • Martin Schmidt
  • Anton Svensson
  • Johannes Thürauf
    • Categories Bilevel Optimization Tags , , , , ,

    We study linear bilevel and pricing problems in which the upper- and lower-level constraints’ right-hand sides are perturbed. In this setting, it is an important question, also for the validity of numerical solution schemes, if the solution-set mapping of the parametric bilevel problem is calm at the zero-perturbation. We provide the complete picture both for … Read more

    Presolving Linear Bilevel Optimization Problems

  • Thomas Kleinert
  • Martin Schmidt
  • Dieter Weninger
  • Julian Manns
    • Categories (Mixed) Integer Linear Programming, Linear Programming Tags , ,

    Linear bilevel optimization problems are known to be strongly NP-hard and the computational techniques to solve these problems are often motivated by techniques from single-level mixed-integer optimization. Thus, during the last years and decades many branch-and-bound methods, cutting planes, or heuristics have been proposed. On the other hand, there is almost no literature on presolving … Read more