Exceptional family and solvability of copositive complementarity problems

作者：Hu Q J^*; Ouyang Z S; Wang Z M

来源：Journal of Mathematical Analysis and Applications, 2012, 388(1): 519-524.

DOI：10.1016/j.jmaa.2011.10.028

• Copositive complementarity problem
• Exceptional family
• Existence theorem

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-Carbone';s condition, Karamardian';s 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.