一类集值映射的方向度量次正则性

在有限维Hilbert空间中，研究连续可微单值映射与连续闭凸集值映射之差的集值映射的度量次正则性问题.首先，在适当的连续性假设条件下，得到了这类集值映射的强度量次正则性的充分条件；然后，研究了这类集值映射在存在某种“单值选择”条件下的方向度量次正则性，并给出了这类集值映射的方向度量次正则性的一些充分条件.

Directional metric subregularity of a class of set-valued mappings

In finite dimensional Hilbert space, the metric subregularity of a set-valued mapping, which is the difference of a continuous differentiable single valued mapping and a continuous closed convex set-valued mapping, is mainly analyzed. Firstly, under the appropriate continuous assumption, a sufficient condition for the strong metric subregularity of this kind of set-valued mappings is obtained; then, under the continuous condition of some “single value selection”, the directional metric subregularity of this type of set-valued mappings are explored, and some sufficient conditions for the directional metric subregularity of this kind of set-valued mappings are obtained.