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A Penalty Branch-and-Bound Method for Mixed-Integer Quadratic Bilevel Problems. Part I: Key Ideas and a Fixed Parameter Setting

In: Operations Research Proceedings 2022

Author

Listed:
  • Andreas Horländer

    (Trier University)

  • Martin Schmidt

    (Trier University)

Abstract

We propose an algorithm for solving bilevel problems with mixed-integer convex-quadratic upper level as well as convex-quadratic and continuous lower level. The method is based on a classic branch-and-bound procedure, where branching is performed on the integer constraints and on the complementarity constraints resulting from the Karush–Kuhn–Tucker reformulation of the lower-level problem. However, instead of branching on constraints as usual, suitably chosen penalty terms are added to the objective function to create new subproblems in the tree. In this first part, we consider a fixed penalty parameter, derive the main ideas, and prove the correctness of the method for this setting.

Suggested Citation

  • Andreas Horländer & Martin Schmidt, 2023. "A Penalty Branch-and-Bound Method for Mixed-Integer Quadratic Bilevel Problems. Part I: Key Ideas and a Fixed Parameter Setting," Lecture Notes in Operations Research, in: Oliver Grothe & Stefan Nickel & Steffen Rebennack & Oliver Stein (ed.), Operations Research Proceedings 2022, chapter 0, pages 139-145, Springer.
    • Handle: RePEc:spr:lnopch:978-3-031-24907-5_17
    DOI: 10.1007/978-3-031-24907-5_17
    as

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