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- W4289702191 abstract "We study the representability of sets that admit extended formulations using mixed-integer 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 mixed-integer 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 mixed-integer representable sets forms an algebra of sets (up to topological closures)." @default.
- W4289702191 created "2022-08-04" @default.
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- W4289702191 date "2018-08-11" @default.
- W4289702191 modified "2023-09-23" @default.
- W4289702191 title "Mixed-integer bilevel representability" @default.
- W4289702191 doi "https://doi.org/10.48550/arxiv.1808.03865" @default.
- W4289702191 hasPublicationYear "2018" @default.
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