NEW CLASSES OF PREINVEX FUNCTIONS AND DIRECTIONAL VARIATIONAL-LIKE INEQUALITIES

Abstract

In this paper, we introduce and study some new classes of preinvex functions
with respect to an arbitrary function k and the bifunction (:; :); which are called the k-preinvex functions. These functions are nonconvex functions and include the preinvex function, convex functions and k-convex as special cases. We study some properties of k-preinvex functions. It is shown that the minimum of k- preinvex functions on the k-invex sets can be characterized by a class of variational inequalities, which is called the k-directional
variational-like inequalities. Using the auxiliary technique, several new inertial type methods for solving the directional variational-like inequalities. Convergence analysis of the proposed methods is considered under suitable conditions. Some open problems are also suggested for
future research.
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