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Unbounded convex sets for non-convex mixed-integer quadratic programming

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Abstract

This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a face of a set in the family. Some fundamental properties of the convex sets are derived, along with connections to some other well-studied convex sets. Several classes of valid and facet-inducing inequalities are also derived.

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Acknowledgments

The first author was supported by the National Science Foundation under grant CCF-0545514 and the second author was supported by the Engineering and Physical Sciences Research Council under grant EP/D072662/1. Thanks are due to two anonymous referees for their helpful corrections and suggestions.

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Correspondence to Adam N. Letchford.

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Research supported in part by NSF Grant CCF-0545514.

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Burer, S., Letchford, A.N. Unbounded convex sets for non-convex mixed-integer quadratic programming. Math. Program. 143, 231–256 (2014). https://doi.org/10.1007/s10107-012-0609-9

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