向量优化中值映射的余切上图可微性

考虑参数向量优化问题MinK|f(w,x)|x∈G(w)},其中fW×X→Y是从赋范线性空间W和X的积到另一个赋范线性空间Y的Hadamard可微单值映射,GW→X是一个集值映射,K∈Y$是一个闭凸点锥.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表示.当约束由等式和不等式确定时,借助于拉格朗日映射,给出了值映射的余切上图导数的另一表示.

Contingent epidifferentiability of the value map in vector optimization

Consider 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 KC Y is a convex closed pointed cone. A representation of contingent epiderivative of the value map is given in terms of the derivative of the objective function and the contingent derivative of the constraint map. An alternative representation in terms of the Lagrangian mapping is obtained in the case when constraints are defined by a system of equalities and inequalities.