The (In)Famous Big-M Technique for Solving Bilevel Programs

Saeed Mohammadi (), Mohammad Reza Hesamzadeh () and Dina Khastieva ()
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Saeed Mohammadi: KTH Royal Institute of Technology, School of Electrical Engineering and Computer Science
Mohammad Reza Hesamzadeh: KTH Royal Institute of Technology, School of Electrical Engineering and Computer Science
Dina Khastieva: KTH Royal Institute of Technology, School of Electrical Engineering and Computer Science

A chapter in Theory, Algorithms, and Experiments in Applied Optimization, 2025, pp 213-240 from Springer

Abstract: Abstract Linear bilevel programs (linear BLPs) have been widely used in computational mathematics and optimization in several applications. Single-level reformulation for linear BLPs replaces the lower-level linear program with its Karush-Kuhn-Tucker optimality conditions and linearizes the complementary slackness conditions using the big-M technique. Although the approach is straightforward, it requires finding the big-M whose computation is recently shown to be NP-hard. This paper presents a disjunctive-based decomposition algorithm which does not need finding the big-Ms, whereas guaranteeing that obtained solution is optimal. Our experience shows promising performance of our algorithm.

Keywords: Bilevel optimization; Parameter-free decomposition; Disjunctive-based decomposition; Bilevel programming problems (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-91357-0_11

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DOI: 10.1007/978-3-031-91357-0_11

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