Domination property and existence of Pareto efficient points in convex vector-valued optimization

Concepts such as convexity, semi-continuity and recession cones are extended in a natural way to vector-valued functions in the preliminaries. The results so obtained are used to study the domination property in the constrained convex vector-valued optimization problem. The paper so obtains, with the first orthant as a domination cone, generalisations of known results on the matter. As by-products, it gives conditions for the existence of Pareto-efficient points.