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Unbounded Convex Sets for Non-Convex Mixed-Integer Quadratic Programming

Samuel Burer (samuel-burer***at***uiowa.edu)
Adam Letchford (a.n.letchford***at***lancaster.ac.uk)

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 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.

Keywords: mixed-integer non-linear programming, global optimisation, polyhedral combinatorics, convex analysis

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Combinatorial Optimization (Polyhedra )

Citation: Eventually published as: S. Burer & A.N. Letchford (2014) Unbounded convex sets for non-convex mixed-integer quadratic programming. Math. Program., 143(1-2), 231-256.

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Entry Submitted: 09/18/2011
Entry Accepted: 09/18/2011
Entry Last Modified: 05/31/2014

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