约束集值优化问题的二阶最优性条件

摘要

给出集值映射二阶导数的定义,并讨论了其相关性质.运用此二阶导数及二阶相依导数,建立了约束集值优化问题的二阶必要最优性条件.在有限维空间中得到了约束集值优化问题的二阶充分最优性条件.%A second-order derivative for set-valued maps was proposed and its properties were discussed. By means of this derivative and second-order contingent derivative, some second-order necessary optimality conditions were established for constrained set-valued optimization problems. And some second-order sufficient optimality conditions were obtained for constrained set-valued optimization problems in finite-dimensional normed spaces.