Weak quasi-invexity of nonsmooth functions

The notions of quasi-1 convexity, weak quasi-convexity and weak quasi-invexity are introduced. The relations among strict quasi-preinvexity, weak quasi-invexity and pseudo-invexity for a nonsmooth function are studied by means of the properties of the Clarke’s generalized subdifferential. As an application of the main results in this work, the relations among quasi-1 convexity, strict quasi-convexity, weak quasi-convexity and pseudo-convexity are established.