Scalarized solutions of set-valued optimization problems and generalized variational-like inequalities

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.