Second-Order Contingent Derivative of the Perturbation Map in Multiobjective Optimization

Here, u is a p-dimensional decision variable, x is an n-dimensional parameter vector, X is a nonempty set-valued map from R to R, which specifies a feasible decision set, and f is an objective map from R × R to R, wherem, n, p are positive integers. The norms of all finite dimensional spaces are denoted by ‖ · ‖. C is a closed convex pointed cone with nonempty interior in R. The cone C induces a partial order ≤C on R, that is, the relation ≤C is defined by