An application of H differentiability to generalized complementarity problems over symmetric cones

In this paper, we focus on a generalized complementarity problems over symmetric cone GSCCP(f,gf,g) when the underlying functions ff and gg are HH-differentiable. By introducing the concepts of relatively uniform Cartesian PP-property, relatively Cartesian P(P0)P(P0)-property, the Cartesian semimonotone (E0E0)-property (strictly Cartesian semimonotone (EE)-property), and the relatively regular point with respect to the merit function Ψ(x)Ψ(x), we extend various similar results proved in GCP(f,g)(f,g) to generalized complementarity problems over symmetric cone GSCCP(f,g)(f,g) and establish various conditions on ff and gg to get a solution to GSCCP(f,g)(f,g).