集值优化问题的二阶最优性条件(英文)

Second-order optimality conditions in set-valued optimization problems

本文提出了集值映射的一种二阶导数,并讨论了其相关性质.运用此二阶导数以及二阶相依导数,作者建立了实赋范空间中集值优化问题的二阶必要最优性条件;同时,在有限维赋范空间中,建立了集值优化问题的二阶充分最优性条件.

In this paper, a second-order derivative for set-valued maps is proposed and its properties are discussed. By using this derivative and second-order contingent derivative, some second-order necessary optimality conditions for set-valued optimization problems in real normed spaces are obtained. Simulta- neously, some second-order sufficient optimality conditions for set-valued optimization problems in fi- nite-dimensional normed spaces are established.