Directional Subdifferentials of the Value Function in Asplund Spaces

Weihao Mao; Jane J. Ye

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arXiv · 2608.20241

Directional Subdifferentials of the Value Function in Asplund Spaces

Weihao Mao·Jane J. Ye

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Abstract

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.

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BibTeX RIS

Weihao Mao, Jane J. Ye. 2026-08-20. Directional Subdifferentials of the Value Function in Asplund Spaces. https://arxiv.org/abs/2608.20241

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