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The binary quadratic knapsack problem maximizes a quadratic objective function subject to a linear capacity constraint. Due to its simple structure and challenging difficulty it has been studied intensively during the last two decades. The present paper gives a survey of upper bounds presented in the literature, and show the relative tightness of several of the bounds. Techniques for deriving the bounds include relaxation from upper planes, linearization, reformulation, Lagrangian relaxation,doi:10.1016/j.dam.2006.08.007 fatcat:jshopbokirfdfiackwmzdawgwq