Localization of complementarity eigenvalues

Let A, B be symmetric n x n real matrices with B positive definite and strictly diagonally dominant. We derive two localization sets for the complementarity eigenvalues of (A, B), the tightest one assuming additionally that A is copositive. This extends He-Liu-Shen sets to the case where B is not the identity. Moreover, we compare the computable bounds obtained from these new sets with the extreme classical generalized eigenvalues.