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See detailCertificates of linear mixed integer infeasibility
Andersen, Kent; Louveaux, Quentin ULiege; Weismantel, Robert

in Operations Research Letters (2008), 36(6), 734-738

We derive a certificate of integral infeasibility for linear systems with equations and inequalities by generating algebraically an outer description of a lattice point free polyhedron that contains the ... [more ▼]

We derive a certificate of integral infeasibility for linear systems with equations and inequalities by generating algebraically an outer description of a lattice point free polyhedron that contains the given integer infeasible system. The extension to the mixed integer setting is also derived. [less ▲]

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See detailUpper-bounds for quadratic 0-1 maximization
Boros, Endre; Crama, Yves ULiege; Hammer, Peter L.

in Operations Research Letters (1990), 9

In this paper, three different approaches are generalised to obtain upper bounds for the maximum of a quadratic pseudo-Boolean function f over [0,1]^n. The original approaches (complementation ... [more ▼]

In this paper, three different approaches are generalised to obtain upper bounds for the maximum of a quadratic pseudo-Boolean function f over [0,1]^n. The original approaches (complementation, majorization and linearization) were introduced by Hammer, Hansen and Simeone. The generalization in this paper yields three upper bounds, Ck, Mk and Lk for each integer k ⩾ 2, where Cn = Ln = Mn is the maximum of f, and C2 = L2 = M2 is the roof duality bound studied by Hammer, Hansen and Simeone. It is proved that Ck = Mk = Lk for all values of k. [less ▲]

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