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