On optimality conditions for a Class of semi-infinite programming

The definitions of some new nonsmooth generalized convex functions were given in terms of concepts of local cone approximation,K-directional derivative and K-subdifferential,that is,K-(F,a,ρ,d)-convex,K-(F,a,ρ,d)-quasiconvex,weak K-(F,a,ρ,d)-quasiconvex,K-(F,a,ρ,d)-pseudoconvex,strict K-(F,a,ρ,d)-pseudo-convex,their generalizations were discussed.Later,the optimality conditions for a class of nonsmooth semi-infinite programming involving these generalized convex functions were studied.