Some Existence Results for Multivalued Complementarity Problems

This paper presents some new results for the existence of a solution to a multivalued complementary problem. These results are derived under a “upper limiting homogeneity” (ULH) property on the multifunction defining the complementarity problem and on a certain closedness/interiority condition. The closedness condition seems to be new in the context of existence proof for the multivalued complementarity problem. We show that this closedness condition is satisfied by the class of polyhedral multifunctions.