Scalarized Solutions of Set-Valued Optimization Problems and Generalized Variational-like Inequalities

Abstract

In this paper by using the scalariation method we introduced the concept of relaxed K-preinvex set-valued maps and obtain some equivalence results of them in terms of normal subdifferential. Also, we consider generalized Minty variational-like inequalities and show that the set of solutions is equal to scalarized set-valued  optimization problems’s solutions under generalized relaxed convexity assumptions.