Upper-bounds for quadratic 0-1 maximization

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.