Second-order contingent derivatives of set-valued mappings with application to set-valued optimization

In this paper, a family of parameterized set‐valued optimization problems, whose constraint set depends on a parameter, are considered. Some calculus rules are obtained for calculating the second‐order contingent derivatives of the composition and sum of two set‐valued mappings. Then, by using these calculus rules, some results concerning second‐order sensitivity analysis are established, and an explicit expression for the second‐order contingent derivative of the (weak) perturbation mapping in the set‐valued optimization problems is obtained.