Variational sets and asymptotic variational sets of proper perturbation map in parametric vector optimization

Abstract

This paper is devoted to the study of sensitivity analysis in terms of variational sets/asymptotic variational sets for parametric vector optimization. The relations between variational sets/asymptotic variational sets, and their proper minima of a set-valued map and that of its profile map are given. Then, the relationships between the above sets of this objective map and that of the proper perturbation map are established. Finally, the formulas for estimating the variational sets/the asymptotic variational sets of the proper perturbation map via the higher-order contingent set/the higher-order asymptotic cone of the constraint map and the higher-order Fréchet derivative of the objective map are also obtained.