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arXiv · 2608.26328

Directional Optimality Conditions for Optimization Problems in Asplund Spaces

Weihao Mao·Jane J. Ye
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Abstract

This paper develops directional necessary optimality conditions for constrained optimization problems in Asplund spaces. Under directional metric subregularity, we first derive a directional optimality condition in terms of limiting subdifferentials. We then introduce sufficient conditions for directional metric subregularity and establish their relationships with directional pseudo-normality and quasi-normality. For systems with joint constraints, we further propose a joint criterion for directional metric subregularity and use it to obtain necessary optimality conditions. The results not only extend several finite-dimensional directional constructions to an Asplund-space setting, but also yield conclusions that are new even in finite dimensions.

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Weihao Mao, Jane J. Ye. 2026-08-26. Directional Optimality Conditions for Optimization Problems in Asplund Spaces. https://arxiv.org/abs/2608.26328

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