Higher-order differential sensitivity for weak vector variational inequalities in terms of tangent derivatives

This paper is devoted to the study of differential sensitivity analysis for weak vector variational inequalities in terms of the higher-order tangent derivatives, which were introduced by J.P. Penot in 2017.We first provide some calculus rules for these derivatives such as composition rule and sum rule, and we obtain some formulas for the tangent derivative of the profile mapping.Then, they are employed to investigate the differential sensitivity for the vector variational inequality problem with the help of gap functions.Several examples are given to illustrate the obtained results.