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Integer quadratic quasi-polyhedra

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

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

Integer Programming and Combinatorial Optimization: Proceedings of the 14th International IPCO Conference. ed. / Friedrich Eisenbrand; F. Bruce Shepherd. Berlin : Springer, 2010. p. 258-270 (Lecture Notes in Computer Science; Vol. 6080).

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

Harvard

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

APA

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

Vancouver

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

Author

Letchford, A N. / Integer quadratic quasi-polyhedra. Integer Programming and Combinatorial Optimization: Proceedings of the 14th International IPCO Conference. editor / Friedrich Eisenbrand ; F. Bruce Shepherd. Berlin : Springer, 2010. pp. 258-270 (Lecture Notes in Computer Science).

Bibtex

@inbook{e8d64e40a432481d960b6f777d88b6b1,
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}",
year = "2010",
doi = "10.1007/978-3-642-13036-6_20",
language = "English",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "258--270",
editor = "Eisenbrand, {Friedrich } and Shepherd, {F. Bruce}",
booktitle = "Integer Programming and Combinatorial Optimization",

}

RIS

TY - CHAP

T1 - Integer quadratic quasi-polyhedra

AU - Letchford, A N

PY - 2010

Y1 - 2010

N2 - 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.

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.

KW - mixed-integer nonlinear programming

U2 - 10.1007/978-3-642-13036-6_20

DO - 10.1007/978-3-642-13036-6_20

M3 - Chapter (peer-reviewed)

T3 - Lecture Notes in Computer Science

SP - 258

EP - 270

BT - Integer Programming and Combinatorial Optimization

A2 - Eisenbrand, Friedrich

A2 - Shepherd, F. Bruce

PB - Springer

CY - Berlin

ER -