This paper presents a generalization of the Arrow, Barankin and Blackwell theorem to locally convex Hausdorff topological vector spaces. Our main result relaxes the requirement that the objective set be compact; we show asymptotic compactness is sufficient, provided the asymptotic cone of the objective set can be separated from the ordering cone by a closed and convex cone. Additionally, we give a similar generalization using Henig efficient points when the objective set is not assumed to be convex. Our results generalize results of A. Gopfert, C. Tammer, and C. Za?linescu to locally convex spaces.