Abstract.
Two approaches that solve the mixed-integer nonlinear bilevel programming problem to global optimality are introduced. The first addresses problems mixed-integer nonlinear in outer variables and C2-nonlinear in inner variables. The second adresses problems with general mixed-integer nonlinear functions in outer level. Inner level functions may be mixed-integer nonlinear in outer variables, linear, polynomial, or multilinear in inner integer variables, and linear in inner continuous variables. This second approach is based on reformulating the mixed-integer inner problem as continuous via its vertex polyheral convex hull representation and solving the resulting nonlinear bilevel optimization problem by a novel deterministic global optimization framework. Computational studies illustrate proposed approaches.
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Gümüş, Z.H., Floudas, C.A. Global optimization of mixed-integer bilevel programming problems. CMS 2, 181–212 (2005). https://doi.org/10.1007/s10287-005-0025-1
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DOI: https://doi.org/10.1007/s10287-005-0025-1