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Amitabh Basu (abasu9jhu.edu) Abstract: We study the representability of sets that admit extended formulations using mixedinteger bilevel programs. We show that feasible regions modeled by continuous bilevel constraints (with no integer variables), complementarity constraints, and polyhedral reverse convex constraints are all finite unions of polyhedra. Conversely, any finite union of polyhedra can be represented using any one of these three paradigms. We then prove that the feasible region of bilevel problems with integer constraints exclusively in the upper level is a finite union of sets representable by mixedinteger programs and vice versa. Further, we prove that, up to topological closures, we do not get additional modeling power by allowing integer variables in the lower level as well. To establish the last statement, we prove that the family of sets that are finite unions of mixedinteger representable sets forms an algebra of sets (up to topological closures). Keywords: Bilevel programming, Mixed Integer programming Category 1: Integer Programming (Other ) Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming ) Citation: Download: [PDF] Entry Submitted: 08/11/2018 Modify/Update this entry  
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