On Classes of Generalized Convex Functions, Farkas-Type Theorems and Lagrangian Duality

In this paper we introduce several classes of generalized convex functions already discussed in the literature and show the relation between those function classes. Moreover, for some of those function classes a Farkas-type theorem is proved. As such this paper unifies and extends results existing in the literature and shows how these results can be used to verify Farkas-type theorems and strong Lagrangian duality results in finite dimensional optimization.