Choquet boundaries and efficiency

This research paper is devoted to establish the coincidence between Choquet boundaries and a new type of approximate efficient points sets in ordered Hausdorff locally convex spaces, being based on the first result established by us concerning such a property as this for Pareto-type efficient points sets and the corresponding Choquet boundaries of non-empty compact sets, with respect to appropriate convex cones of real, increasing and continuous functions. Thus, the main result represents a strong connection between two great fields of mathematics: The Axiomatic Theory of Potential and Vector Optimization. The present study contains also important relationships concerning strong optimization and approximate efficiency, interesting examples, pertinent remarks and some open problems.