Calculus rules of generalized proper $\epsilon$-subdifferential for vector valued mappings and applications

This paper deals with a new concept of subdifferential defined in the Pareto sense and adapted to nonconvex vector mappings, called generalized proper -subdifferential.Some existence theorems and properties are discussed.We establish some formulas of the generalized proper -subdifferential for the sum and the difference of two vector valued mappings.As an application of the calculus rules, we establish necessary and sufficient optimality conditions for a constrained vector optimization problem with the difference of two vector valued mappings.