Abstract: The concept of near preinvexity was introduced, which is weaker than preinvexity. An example was given to illustrate that near preinvexity is a properly generalization of preinvexity. With the help of the properties of generalized contingent epiderivative, a necessary optimality condition was established for setvalued optimization to attain its weakly efficient elements. When objective function is nearly preinvex, for weakly efficient elements an optimality sufficient condition was also derived.

Key words: near preinvexity, generalized contingent epiderivative, weakly efficient element