Global optimization of mixed-integer bilevel programming problems

Global optimization of mixed-integer nonlinear bilevel optimization problems is addressed using a novel technique. For problems where integer variables participate in both inner and outer problems, the outer level may involve general mixed-integer nonlinear functions. The inner level may involve functions that are mixed-integer nonlinear in outer variables, linear, polynomial, or multilinear in inner integer variables, and linear in inner continuous variables. The technique is based on reformulating the mixed-integer inner problem as continuous via its convex hull representation (Sherali and Adams 1990; 1994) and solving the resulting nonlinear bilevel problem by a novel deterministic global optimization framework. For problems where the integer variables are only in the outer problem, both the inner and outer problems may be nonlinear in both inner and outer variables. These are solved by a direct extension of the global optimization framework of Gümüş and Floudas (2001).