集值优化问题严有效解的高阶最优性条件

在实赋范线性空间中考虑集值优化问题的严有效性.当目标函数和约束函数均为锥凹集值映射时,利用凸集分离定理并借助集值映射高阶导数给出了带约束集值优化问题取得严最大有效解的Fritz John最优性必要条件,并用构造性方法证明了集值优化问题取得严最大有效解的充分条件。

Higher-Order Optimality Conditions of Strictly Efficient Solutions for Set-Valued Optimization Problem

The strict efficiency of set valued optimization was considered in real normed spaces. When both objective function and constraint function were concave, Fritz John type necessary optimality condition was established for set valued optimization problem with constraint to attain its strict maximal solution with higher order derivatives and separation theorem for convex sets. With the properties of base functional and the constructive method, sufficient optimality condition was also derived.