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**Integer quadratic quasi-polyhedra.** / Letchford, A N.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed)

Letchford, AN 2010, Integer quadratic quasi-polyhedra. in F Eisenbrand & FB Shepherd (eds), *Integer Programming and Combinatorial Optimization: Proceedings of the 14th International IPCO Conference.* Lecture Notes in Computer Science, vol. 6080, Springer, Berlin, pp. 258-270, 14th International Conference, IPCO 2010, Lausanne, Switzerland, 9/06/10. https://doi.org/10.1007/978-3-642-13036-6_20

Letchford, A. N. (2010). Integer quadratic quasi-polyhedra. In F. Eisenbrand, & F. B. Shepherd (Eds.), *Integer Programming and Combinatorial Optimization: Proceedings of the 14th International IPCO Conference *(pp. 258-270). (Lecture Notes in Computer Science; Vol. 6080). Berlin: Springer. https://doi.org/10.1007/978-3-642-13036-6_20

Letchford AN. Integer quadratic quasi-polyhedra. In Eisenbrand F, Shepherd FB, editors, Integer Programming and Combinatorial Optimization: Proceedings of the 14th International IPCO Conference. Berlin: Springer. 2010. p. 258-270. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-642-13036-6_20

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title = "Integer quadratic quasi-polyhedra",

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.",

keywords = "mixed-integer nonlinear programming",

author = "Letchford, {A N}",

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AB - 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.

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