Upper-bounds for quadratic 0-1 maximization

Authors:
E. Boros;Y. Crama;P. L. Hammer
Affiliations:
RUTCOR - Rutgers Center for Operations Research, Rutgers University, New Brunswick, NJ, USA;Department of Quantitative Economics, University of Limburg, Maastricht, The Netherlands;RUTCOR - Rutgers Center for Operations Research, Rutgers University, New Brunswick, NJ, USA
Venue:
Operations Research Letters
Year:
1990

Citing 2
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Abstract

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 [9]. The generalization in this paper yields three upper bounds, C"k, M"k and L"k for each integer k = 2, where C"n = L"n = M"n is the maximum of f, and C"2 = L"2 = M"2 is the roof duality bound studied in [9]. It is proved that C"k = M"k = L"k for all values of k.