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