发表机构
Brandenburgische Technische Universität Cottbus–Senftenberg（勃兰登堡理工大学科特布斯-森夫滕贝格）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明凸泛函的强-强二次上导数与其共轭的弱-*二次上导数等价，并据此简化弱-*二阶次导数的计算，该导数对无间隙二阶最优性条件至关重要，且对空间设置变化具有不变性。
AI 中文摘要
我们证明（在若干温和假设下）一个凸泛函的强-强二次上导数等价于其共轭泛函的弱-*二次上导数。此外，相应的次导数（在缩放意义下）互为共轭。该结果可用于简化弱-*二阶次导数的计算，而后者是无间隙二阶最优性条件中的关键要素。我们还证明，在底层函数空间设置的适当变化下，弱-*二阶次导数保持不变。
英文摘要
We prove (under some mild assumptions) that the strong-strong twice epidifferentiability of a convex functional is equivalent to the weak-$\star$ twice epidifferentiability of its conjugate functional. Further, the corresponding subderivatives are (up to scaling) conjugates of each other. This result can be used to facilitate the computation of weak-$\star$ second subderivatives, which are crucial ingredients in no-gap second-order optimality conditions. We also show that weak-$\star$ second subderivatives are invariant under suitable changes of the underlying function space setting.
