A single-level reformulation of mixed integer bilevel programming problems |
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Authors: | Chuanjia Li Lei Guo |
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Affiliation: | 1. Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200030, China;2. Sino-US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai 200030, China |
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Abstract: | This paper focuses on the single-level reformulation of mixed integer bilevel programming problems (MIBLPP). Due to the existence of lower-level integer variables, the popular approaches in the literature such as the first-order approach are not applicable to the MIBLPP. In this paper, we reformulate the MIBLPP as a mixed integer mathematical program with complementarity constraints (MIMPCC) by separating the lower-level continuous and integer variables. In particular, we show that global and local minimizers of the MIBLPP correspond to those of the MIMPCC respectively under suitable conditions. |
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Keywords: | Mixed integer bilevel program Mixed integer program Mathematical program with complementarity constraints |
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