LL-invex-infine functions and applications

We introduce a new concept of convexity-affineness type of vector functions. The class of vector functions satisfying our definition is wider than some of the corresponding ones known in the literature. Exploiting this concept we first study the Gordan type alternative theorem and then establish a characterization for Geoffrion proper efficient solutions of a multiobjective optimization problem via Lagrange multiplier rules and the limiting/Mordukhovich subdifferential of real-valued functions.