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.
The first author thanks the DFG for their support within RTG 2126 “Algorithmic Optimization”. Both authors kindly acknowledge the support of RHRK.
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References
Horländer, A., & Schmidt, M. (2022). A penalty branch-and-bound method for mixed-integer quadratic bilevel problems. Part I: Key ideas and a fixed parameter setting.
Kleinert, T., & Schmidt, M. (2023). Why there is no need to use a big-\(M\) in linear bilevel optimization: A computational study of two ready-to-use approaches. Computational Management Science.
Kleinert, T., & Schmidt, M. (2021). Computing feasible points of bilevel problems with a penalty alternating direction method. INFORMS Journal on Computing, 33(1), 198–215.
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Horländer, A., Schmidt, M. (2023). A Penalty Branch-and-Bound Method for Mixed-Integer Quadratic Bilevel Problems. Part II: Penalty Updates and Numerical Results. In: Grothe, O., Nickel, S., Rebennack, S., Stein, O. (eds) Operations Research Proceedings 2022. OR 2022. Lecture Notes in Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-031-24907-5_18
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DOI: https://doi.org/10.1007/978-3-031-24907-5_18
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