Optimality Conditions for Static Programming with Generalized Convexity

The definitions of generalized pseudoconvex,generalized quasiconvex and its stri ctly generalized convexity were presented for the static programming at locally star -shaped set using the concept of right-upper derivative and the concept of sub linear. The sufficient and necessary conditions of the static programming were d erived in terms of a generalized Lemma in this paper. The results obtained are u seful for the further study on the duality of static programming and cover many already known conditions.