Holger Heitsch

On Convex Lower-Level Black-Box Constraints in Bilevel Optimization with an Application to Gas Market Models with Chance Constraints

  • Holger Heitsch
  • René Henrion
  • Thomas Kleinert
  • Martin Schmidt
    • Categories Applications - OR and Management Sciences, Cutting Plane Approaches, Stochastic Programming Tags , , , ,

    Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this … Read more

    Solving joint chance constrained problems using regularization and Benders’ decomposition

  • Lukáš Adam
  • Holger Heitsch
  • René Henrion
  • Martin Branda
    • Categories Stochastic Programming

    We consider stochastic programs with joint chance constraints with discrete random distribution. We reformulate the problem by adding auxiliary variables. Since the resulting problem has a non-regular feasible set, we regularize it by increasing the feasible set. We solve the regularized problem by iteratively solving a master problem while adding Benders’ cuts in a slave … Read more