Approximate feasibility

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

    On a Computationally Ill-Behaved Bilevel Problem with a Continuous and Nonconvex Lower Level

  • Yasmine Beck
  • Martin Schmidt
  • Johannes Thürauf
  • Daniel Bienstock
    • Categories Global Optimization, Nonlinear Optimization Tags , , ,

    It is well known that bilevel optimization problems are hard to solve both in theory and practice. In this paper, we highlight a further computational difficulty when it comes to solving bilevel problems with continuous but nonconvex lower levels. Even if the lower-level problem is solved to ɛ-feasibility regarding its nonlinear constraints for an arbitrarily … Read more