Asplund空间中方向上导数和序列法紧性质分析法则

研究了广义微分结构中的集合方向Mordukhovich法锥、集值映射的方向上导数，以及集合和集值映射的方向序列法紧性的分析法则. 基于集合方向Mordukhovich法锥的交集法则，在方向内半紧性假设下，建立了集合的方向Mordukhovich法锥、集值映射的方向上导数的分析法则.此外，借助Asplund乘积空间中集合的方向序列法紧性的交集法则， 在方向内半紧性和相应的规范条件下，建立了集合和集值映射的(部分)方向序列法紧性的加法、逆像、复合等法则.

Calculus of Normal Cones and Coderivatives Under the Assumption of Directional Inner Semicompactness in Asplund Spaces

The directional Mordukhovich normal cones of sets,directional Mordukhovich coderivatives of set-valued mapping,and directional sequential normal compactness of sets and set-valued mapping in the framework of generalized differentiation were studied.Based on the intersection rule for directional Mordukhovich normal cones of sets,the calculus rules on directional Mordukhovich normal cones of sets and directional Mordukhovich coderivatives of setvalued mapping were established under some directional inner semicompactness assumptions.Furthermore,in virtue of the intersection rule for directional sequential normal compactness of sets,the sum rule,inverse mapping rule,and composition rule for directional (partial) sequential normal compactness of sets and set-valued mapping were presented under some directional inner semicompactness assumptions and suitable qualification conditions.