Knapsack interdiction

An Extension of the Bertsimas & Sim Result for Discrete, Linear, and Γ-Robust Min-Max Problems

  • Yasmine Beck
  • Ivana Ljubić
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Robust Optimization Tags , , , ,

    Due to their nested structure, bilevel problems are intrinsically hard to solve – even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. We provide an extension of the … Read more

    Exact Methods for Discrete Γ-Robust Interdiction Problems with an Application to the Bilevel Knapsack Problem

  • Yasmine Beck
  • Ivana Ljubić
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Robust Optimization Tags , , , ,

    Developing solution methods for discrete bilevel problems is known to be a challenging task – even if all parameters of the problem are exactly known. Many real-world applications of bilevel optimization, however, involve data uncertainty. We study discrete min-max problems with a follower who faces uncertainties regarding the parameters of the lower-level problem. Adopting a … Read more