Home > Research > Publications & Outputs > Integer quadratic quasi-polyhedra
View graph of relations

Integer quadratic quasi-polyhedra

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter (peer-reviewed)peer-review



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.