Invexity and pseudoinvexity in multiobjective programming

Resumen

In this communication, we will center on Multiobjective Programming Problems without and with constraints, (MP) and (CMP), respectively. A vector critical point is a necessary condition for a feasible point of (MP) to be ecient solution or a weakly ef- cient solution. It is an interesting problem to look for the class of functions for which the converse holds. For this purpose, we present some types of pseudoinvex functions. We improve recent results and prove that pseudoinvexity is a necessary and sucient condition in order that all vector critical points are ecient and weakly ecient solutions of (MP), and study the existing relationships among these functions by some examples. We extend the previous results by the introduction of KT/FJ-pseudoinvexity-I/II. For (CMP), we prove that in order for Kuhn-Tucker or Fritz-John points to be ecient or weakly ecient solutions it is necessary and sucient that the multiobjective problem functions belong to these new classes.