Exceptional family and solvability of copositive complementarity problems

In this paper, by extending the concept of exceptional family to complementarity problems over the cone of symmetric copositive real matrices, we propose an existence theorem of a solution to the copositive complementarity problem. Extensions of Isac–Carboneʼs condition, Karamardianʼs condition, weakly properness and coercivity are also introduced. Several applications of these results are presented, and we prove that without exceptional family is a sufficient and necessary condition for the solvability of pseudomonotone copositive complementarity problems.