不等式约束的向量优化中值映射的余切上图导数

Contingent Epiderivative of the Value Map in Vector Optimization of Inequality Constraint

考虑如下的参数向量优化问题minK{f(w,x)|x∈X,g(w,x)∈C},这里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,K Y是一个尖闭凸锥,C是Banach空间Z中的一个尖闭凸锥,g:W×X→Z是一个Fréchet可微的映射.借助目标函数的导数、约束映射的余切导数及拉格朗日映射给出了值映射的余切上图导数的两个表示.

Consider the parametrized minimization problem min K{f（w,x）｜x∈X,g（w,x）∈C}, where f：W×X→Y a Hadamard-differentiable single-Valued map from the product of two normed spaces W and X to another normed space Y,K∩Y is a convex closed pointed cone. C is a closed convex pointed cone of a Banach space Z, g：W×X→Z is a Fr6chet differentiable mapping. Two representations of contingent epiderivative of the value map is given in terms of the derivative of the objective function, the contingent derivative of the constraint map and the Lagrangian mapping.