Abstract: In this paper, the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced. And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps, used new methods, the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.

Key words: nearly generalized cone-subconvexlikeness, set-valued map, ε-super e?cient
solution, lagrange multiplier