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

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<mark>Journal publication date</mark>1/02/2014
<mark>Journal</mark>Mathematical Programming
Issue number1-2
Number of pages26
Pages (from-to)231-256
Publication StatusPublished
Early online date19/10/12
<mark>Original language</mark>English


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.