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Computational Linear Bilevel Optimization

In: Operations Research Proceedings 2022

Author

Listed:
  • Thomas Kleinert

    (Friedrich-Alexander Universität Erlangen-Nürnberg, Discrete Optimization)

Abstract

In this article, we summarize a subset of the findings of the cumulative dissertation “Algorithms for Mixed-Integer Bilevel Problems with Convex Followers”; see [4]. First, we present a result that renders the application of the well-known and widely used big-M reformulation of linear bilevel problems infeasible for many practical applications. Second, we present valid inequalities and demonstrate that an SOS1-based approach is a competitive alternative to the error-prone big-M method in case both approaches are equipped with these valid inequalities. Third, we introduce a penalty alternating direction method, which computes (close-to-)optimal feasible points in extremely short computation times and outperforms a state-of-the-art local method.

Suggested Citation

  • Thomas Kleinert, 2023. "Computational Linear Bilevel Optimization," Lecture Notes in Operations Research, in: Oliver Grothe & Stefan Nickel & Steffen Rebennack & Oliver Stein (ed.), Operations Research Proceedings 2022, chapter 0, pages 11-17, Springer.
  • Handle: RePEc:spr:lnopch:978-3-031-24907-5_2
    DOI: 10.1007/978-3-031-24907-5_2
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