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A Penalty Branch-and-Bound Method for Mixed-Integer Quadratic Bilevel Problems. Part II: Penalty Updates and Numerical Results

In: Operations Research Proceedings 2022

Author

Listed:
  • Andreas Horländer

    (Trier University)

  • Martin Schmidt

    (Trier University)

Abstract

In the first part of this paper, we propose a penalty branch-and-bound method for solving bilevel problems with mixed-integer convex-quadratic upper level as well as convex-quadratic and continuous lower level and analyze the method for a fixed penalty parameter. In this second part, we extend the algorithm and its analysis towards iteratively adapted penalty parameters, prove the correctness of this extended method, and show its applicability by some first numerical results.

Suggested Citation

  • Andreas Horländer & Martin Schmidt, 2023. "A Penalty Branch-and-Bound Method for Mixed-Integer Quadratic Bilevel Problems. Part II: Penalty Updates and Numerical Results," Lecture Notes in Operations Research, in: Oliver Grothe & Stefan Nickel & Steffen Rebennack & Oliver Stein (ed.), Operations Research Proceedings 2022, chapter 0, pages 147-153, Springer.
    • Handle: RePEc:spr:lnopch:978-3-031-24907-5_18
    DOI: 10.1007/978-3-031-24907-5_18
    as

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