Exceptional family and solvability of the second-order cone complementarity problems

In this paper, we introduce a concept of exceptional family for second-order cone complementarity problems (denoted by SOCCP), which is the particular case of the concept of exceptional family of elements introduced by Isac and Carbone (1999) [25] for the nonlinear complementarity problems. And the exceptional family for second-order cone complementarity problems has some pretty unique properties. Furthermore, we propose a new sufficient existence condition of a solution to SOCCP and give a particular example to show that the new condition is not stronger than known Isac-Carbone's condition.