引进了$\alpha$-阶近似锥-弧连通集值映射, 举例说明了它是锥-弧连通集值映射的真推广. 借助$Y$-切锥引进了广义$Y$-切上图导数, 讨论了它与广义切上图导数的关系. 当目标函数为$\alpha$-阶近似锥-弧连通集值映射时, 得到集值优化取得弱有效元的充分和必要条件.

The concept of $\alpha$-order nearly cone-arcwise connected set-valued mapping is introduced. An example is given to illustrate that the $\alpha$-order nearly cone-arcwise connected set-valued mapping is a proper generalization of the cone arcwise connected set-valued mapping. With the help of $Y$-contingent cone, generalized $Y$-contingent epiderivative is introduced, and the relationship between generalized $Y$-contingent epiderivative and generalized contingent epiderivative is discussed. When objective function is $\alpha$-order nearly cone-arcwise connected, for weakly efficient elements optimality sufficient and necessary conditions are also established.