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

Burer, Samuel and Letchford, Adam (2014) Unbounded convex sets for non-convex mixed-integer quadratic programming. Mathematical Programming, 143 (1-2). pp. 231-256. ISSN 0025-5610

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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.

Item Type: Article
Journal or Publication Title: Mathematical Programming
Uncontrolled Keywords: mixed-integer nonlinear programming ; global optimisation ; polyhedral combinatorics
Subjects: H Social Sciences > HB Economic Theory
Departments: Lancaster University Management School > Management Science
ID Code: 58801
Deposited By: ep_importer_pure
Deposited On: 03 Oct 2012 10:28
Refereed?: Yes
Published?: Published
Last Modified: 26 Jun 2014 12:45
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/58801

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