Asplund空间中值函数的方向次微分
Directional Subdifferentials of the Value Function in Asplund Spaces
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中文总结 AI 辅助
本文在Asplund空间中建立变分框架，拓展方向非光滑分析至无限维空间，推导值函数的方向次微分上估计，为无限维层级系统灵敏度分析提供精细分析基础。
中文摘要 AI 辅助
值函数的方向次微分提供了最优值对扰动响应的定量度量。现有结果大多局限于有限维情形，本文在Asplund空间中构建了一套完整的变分框架，建立了基本的方向微积分规则，将方向非光滑分析拓展至无限维空间。为解决无限维空间中有界集缺乏紧性的问题，本文引入了一种新的方向条件，在该条件下推导了值函数的方向极限次微分和奇异次微分的上估计。这些结果为无限维层级系统的灵敏度分析提供了更精细的分析基础。
英文摘要
Directional subdifferentials of the value function provide a quantitative measure of optimal value response to perturbations. While existing results are largely limited to finite-dimensional settings, this paper develops a comprehensive variational framework in Asplund spaces. We establish essential directional calculus rules, extending directional nonsmooth analysis to infinite dimensions. To address the lack of compactness of bounded sets in infinite-dimensional spaces, we introduce a new directional condition, under which we derive upper estimates for directional limiting and singular subdifferentials of the value function. These results provide a refined analytical foundation for sensitivity analysis in infinite-dimensional hierarchical systems.
