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arXiv · 2203.06069

A New Computational Approach for Solving Linear Bilevel Programs Based on Parameter-Free Disjunctive Decomposition

Saeed Mohammadi·Mohammad Reza Hesamzadeh·Steven A. Gabriel·Dina Khastieva
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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.

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Saeed Mohammadi, Mohammad Reza Hesamzadeh, Steven A. Gabriel, Dina Khastieva. 2022-03-11. A New Computational Approach for Solving Linear Bilevel Programs Based on Parameter-Free Disjunctive Decomposition. https://arxiv.org/abs/2203.06069

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