论文标题
基于Fréchet二阶细分的最佳条件
Optimality conditions based on the Fréchet second-order subdifferential
论文作者
论文摘要
本文着重于二阶必需的最佳条件，用于在Banach空间上的优化问题。对于在经典环境中的问题，目标函数为$ c^2 $ -Smooth，我们表明，如果约束集是广义的多面体凸，则加强二阶必要的最佳条件是有效的。对于新设置中的问题，仅认为目标函数为$ c^1 $ - 平滑且约束集是广义的多面体凸，我们建立了基于目标函数的二阶二阶副尺寸的尖锐二阶必需的最佳条件，并建立了二阶连饰和二阶较小的相导。给出了三个示例，以表明使用的假设对于新定理至关重要。我们的二阶必要最佳条件会完善并扩展几个现有结果。
This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $C^2$-smooth, we show that strengthened second-order necessary optimality conditions are valid if the constraint set is generalized polyhedral convex. For problems in a new setting, where the objective function is just assumed to be $C^1$-smooth and the constraint set is generalized polyhedral convex, we establish sharp second-order necessary optimality conditions based on the Fréchet second-order subdifferential of the objective function and the second-order tangent set to the constraint set. Three examples are given to show that the used hypotheses are essential for the new theorems. Our second-order necessary optimality conditions refine and extend several existing results.
