A single-level reformulation of mixed integer bilevel programming problems

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.