集值优化Benson真有效元的二阶刻画

Second-order characterizations on Benson proper efficient element of set-valued optimization

引进了一种新的二阶组合切锥,利用它引进了一种新的二阶组合切导数,称为二阶组合径向切导数,并讨论了它的性质及它与二阶组合切导数的关系,借助二阶径向组合切导数,分别建立了集值优化取得Benson真有效元的最优性充分和必要条件.

This paper introduced a new kind of second-order tangent cone, and related second-order tangent derivative, termed as second-order radial composed tangent derivative. Some properties of second-order radial composed tangent derivative and its relationship to second-order composed tangent derivative are discussed. Sufficient and necessary optimality conditions are established respectively for a Benson proper efficient element of set-valued optimization by second-order radial tangent derivative.