Sensitivity and stability for the second‐order contingent derivative of the proper perturbation map in vector optimization

Sensitivity analysis and stability analysis in vector optimization are dealt with in this paper. First, some relationships between the second‐order contingent derivative of a set‐valued map and its profile map are obtained. Secondly, the upper semicontinuity and lower semicontinuity of second‐order contingent derivatives of set‐valued maps are established. Finally, by virtue of the second‐order contingent derivative of set‐valued maps, quantitative information and qualitative information on the behavior of the proper perturbation map are obtained.