Abstract
We study a bilevel programming problem (BLPP) with a maximin lower level problem which is non-smooth and sometimes even non-convex. We reformulate such a non-smooth BLPP as a tractable single-level optimization problem and provide a verifiable sufficient condition to guarantee that the reformulated model is equivalent to the original one. We show that using the proposed approach, some type of BLPP can be reformulated as a simple convex optimization problem. It significantly reduces the computational complexity of the BLPP. The proposed approaches can be widely used for decision-making problems. We apply them to assembly and newsvendor problems in this paper.
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This research was supported by JSPS KAKENHI Grant No. 15K03599.
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Zhu, X., Guo, P. Single-level reformulations of a specific non-smooth bilevel programming problem and their applications. Optim Lett 14, 1393–1406 (2020). https://doi.org/10.1007/s11590-019-01444-7
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DOI: https://doi.org/10.1007/s11590-019-01444-7