向量优化中值映射的余切上图导数的一个表示

A representation of contingent epiderivative of the value map in vector optimization

对于参数向量优化问题minK{f(w,x)|x∈G(w)},其中f:W×X→Y是从赋范空间W和X的积到另一个赋范空间Y的Hadamard可微的单值映射,G:W→X是一个集值映射,KY是一个尖闭凸锥.借助目标函数的导数和约束映射的余切导数,给出了值映射的余切上图导数的一个表示.

Considered the parametrized minimization problem minK {f（w, x） ] x ∈ G（w）}, where f ： W × X → Y is a Hadamard-differentiable single-valued map from the product of two normed spaces W and X to another normed space Y, G ： W → X is a feasible set-valued map, and K belong to Y is a convex closed pointed cone. A representation of contingent epiderivative of the value map was given in terms of the derivative of the objective function and the contingent derivative of the constraint map.