Integer quadratic quasi-polyhedra

Authors:
Adam N. Letchford
Affiliations:
Department of Management Science, Lancaster University, Lancaster, United Kingdom
Venue:
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Year:
2010

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Abstract

This paper introduces two fundamental families of ‘quasi-polyhedra' — polyhedra with a countably infinite number of facets — that arise in the context of integer quadratic programming. It is shown that any integer quadratic program can be reduced to the minimisation of a linear function over a quasi-polyhedron in the first family. Some fundamental properties of the quasi-polyhedra are derived, along with connections to some other well-studied convex sets. Several classes of facet-inducing inequalities are also derived. Finally, extensions to the mixed-integer case are briefly examined.