AI 中文总结
本文针对Asplund空间约束优化问题，在方向度量次正则性条件下推导方向最优性条件，建立其与相关正规性的关系，提出联合约束下的方向度量次正则性判据，推广有限维结果并获新结论。
AI 中文摘要
本文针对Asplund空间中的约束优化问题建立方向必要最优性条件。在方向度量次正则性条件下，我们首先基于极限次微分推导得到一个方向最优性条件；随后给出方向度量次正则性的充分条件，并建立其与方向伪正规性、拟正规性的关系。对于含联合约束的系统，我们进一步提出方向度量次正则性的联合判据，并将其用于推导必要最优性条件。所得结果不仅将若干有限维的方向构造推广至Asplund空间框架，且部分结论在有限维情形下也是全新的。
英文摘要
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.
