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

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Unbounded convex sets for non-convex mixed-integer quadratic programming. / Burer, Samuel; Letchford, Adam.
In: Mathematical Programming, Vol. 143, No. 1-2, 01.02.2014, p. 231-256.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Burer, S & Letchford, A 2014, 'Unbounded convex sets for non-convex mixed-integer quadratic programming', Mathematical Programming, vol. 143, no. 1-2, pp. 231-256. https://doi.org/10.1007/s10107-012-0609-9

APA

Burer, S., & Letchford, A. (2014). Unbounded convex sets for non-convex mixed-integer quadratic programming. Mathematical Programming, 143(1-2), 231-256. https://doi.org/10.1007/s10107-012-0609-9

Vancouver

Burer S, Letchford A. Unbounded convex sets for non-convex mixed-integer quadratic programming. Mathematical Programming. 2014 Feb 1;143(1-2):231-256. Epub 2012 Oct 19. doi: 10.1007/s10107-012-0609-9

Author

Burer, Samuel ; Letchford, Adam. / Unbounded convex sets for non-convex mixed-integer quadratic programming. In: Mathematical Programming. 2014 ; Vol. 143, No. 1-2. pp. 231-256.

Bibtex

@article{c6caa3f5d6934f14bd0553edaeeba55e,
title = "Unbounded convex sets for non-convex mixed-integer quadratic programming",
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.",
keywords = "mixed-integer nonlinear programming, global optimisation, polyhedral combinatorics",
author = "Samuel Burer and Adam Letchford",
year = "2014",
month = feb,
day = "1",
doi = "10.1007/s10107-012-0609-9",
language = "English",
volume = "143",
pages = "231--256",
journal = "Mathematical Programming",
issn = "0025-5610",
publisher = "Springer-Verlag GmbH and Co. KG",
number = "1-2",

}

RIS

TY - JOUR

T1 - Unbounded convex sets for non-convex mixed-integer quadratic programming

AU - Burer, Samuel

AU - Letchford, Adam

PY - 2014/2/1

Y1 - 2014/2/1

N2 - 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.

AB - 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.

KW - mixed-integer nonlinear programming

KW - global optimisation

KW - polyhedral combinatorics

U2 - 10.1007/s10107-012-0609-9

DO - 10.1007/s10107-012-0609-9

M3 - Journal article

VL - 143

SP - 231

EP - 256

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1-2

ER -