On strongly degenerate complementary cones and solution rays

In this paper the authors show that if A is a matrix in the class of matrices E(d), for a d∈Rⁿ,d∈0, introduced by Garcia, then the boundary of the set of q∈Rⁿ for which the linear complementarity problem (q,A) has a solution is equal to the union of all strongly degenerate cones of (I,¸-A). This is a generalization of a similar result for copositive plus matrices observed by Cottle. The authors also study some related questions.