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The complementarity knapsack problem (CKP) is a knapsack problem withreal-valued variables and complementarity conditions between pairs of itsvariables. We extend the polyhedral studies of De Farias et al. for CKP, byproposing three new families of cutting-planes that are all obtained from acombinatorial concept known as a pack. Sufficient conditions for theseinequalities to be facet-defining, based on the concept of a maximal switchingpack, are also provided. Moreover, we answer positively a conjecture by deFarias et~al.~about the separation complexity of the inequalities introduced intheir work, and propose efficient separation algorithms for our newly definedcutting-planes.

New Classes of Facets for Complementarity Knapsack Problems