Computational Linear Bilevel Optimization

Thomas Kleinert ()
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Thomas Kleinert: Friedrich-Alexander Universität Erlangen-Nürnberg, Discrete Optimization

Chapter Chapter 2 in Operations Research Proceedings 2022, 2023, pp 11-17 from Springer

Abstract: 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.

Keywords: Bilevel optimization; Computational optimization; Mixed-integer programming (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnopch:978-3-031-24907-5_2

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DOI: 10.1007/978-3-031-24907-5_2

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