In this paper, we introduce the concept of exceptional family to implicit semidefinite complementarity problems and implicit copositive complementarity problems. Based on the notion of the exceptional family of elements, we prove that the nonexistence of exceptional family of elements is a sufficient condition for the existence theorem of implicit semidefinite complementarity problems and the implicit copositive complementarity problems. The condition is also necessary for relatively pseudomonotone operators to implicit semidefinite complementarity problems. Our results generalize the corresponding results of Isac et al. (1997) and extend the results of Zhang (2008), Hu et al. (2012), Huang and Ma (2014) and Bulavsky et al. (2001). Moreover, we also present some theorems correlated to the structure and strict feasibility of implicit semidefinite complementarity problem. In our analysis, the new concept of exceptional family plays a vital role for the solvability of implicit semidefinite and implicit copositive complementarity problems.

在本文中，我们将例外族的概念引入隐式半定互补问题和隐式共正互补问题。基于超常元素族的概念，我们证明了超常元素族的不存在是隐式半定互补问题和隐合正互补问题存在定理的充分条件。对于相对伪单调算子隐式半定互补问题，该条件也是必要的。我们的结果概括了Isac等人的相应结果。（1997年）和扩展张（2008年）的结果，胡等。（2012），Huang和Ma（2014）和Bulavsky等。（2001）。此外，我们还提出了一些与隐式半定互补问题的结构和严格可行性有关的定理。在我们的分析中，特殊家庭的新概念对于隐式半定和隐式正互补问题的可解决性起着至关重要的作用。