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In locally convex Hausdorff topological vector spaces, ε-strongly efficient solutions for vector optimization with set-valued maps are discussed. Firstly, ε-strongly efficient point of set is introduced. Secondly, under the nearly cone-subconvexlike set-valued maps, the theorem of scalarization for vector optimization is obtained. Finally, optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.