Proper, reflecting and absorbing facts of complementary cones

A common approach in studying the linear complementarity problem is via the geometry of the complementary cones. In the case of nondegeneracy, the concept of a ‘proper facet’ and a ‘reflecting facet’ have proven useful. This paper extends these concepts to the degenerate case. Under degeneracy, a facet may turn out to be neither proper nor reflecting, but, a third type which we designate as ‘absorbing’. Previous results in this area can be easily extended using these more general definitions.