中文摘要：

在实赋范线性空间中考虑集值优化问题的强有效性．借助Henig扩张锥和基泛函的性质，利用广义二阶锥方向相依导数，得到受约束于集值映射的优化问题，取得强有效元的二阶最优性必要条件．当目标函数为近似锥一次类凸映射时，利用强有效点的标量化定理，得到集值优化问题，取得强有效元的二阶充分条件．

英文摘要：

The strong efficiency for set-valued optimization is considered in real normed spaces. With the help of the properties of Henig dilating cone and base functional, by applying generalized second-order cone-directed contingent derivates, a second-order optimality necessary condition is established for a pair to be a strongly efficient element of set-valued optimization whose constraint condition is determined by a set-valued mapping. When objective function is nearly cone-subconvexlike, with the scalarization theorem for a strongly efficient point an a pair to be a strongly efficient element optimality sufficient condition is also derived for of set-valued optimization.