As a variant of metric subregularity, pseudo metric subregularity is studied via general limit critical sets using the techniques of variational analysis. In terms of limit critical sets, we provide some sufficient conditions for the validity of pseudo/Hölder metric subregularity. Usually, the property of pseudo metric subregularity is not stable under small smooth perturbation. We provide a characterization for pseudo metric subregularity to be stable under small \(C^{1,p}\) smooth perturbation. In particular, some existing results on metric subregularity are extended to pseudo metric subregularity. Finally, we consider the pseudo weak sharp minimizer of a proper lower semicontinuous function and its relation with pseudo metric subregularity of the corresponding subdifferential mapping.

作为度量次规则性的一种变体，使用变分分析技术通过一般极限临界集研究伪度量次规则性。在极限临界集方面，我们为伪/Hölder度量次正则性的有效性提供了一些充分条件。通常，伪度量次正则性在小平稳扰动下不稳定。我们提供了伪度量次正则性在小\（C ^ {1，p} \）平稳扰动下稳定的特征。特别是，一些关于度量次规则性的现有结果已扩展到伪度量次规则性。最后，我们考虑了适当的下半连续函数的伪弱尖锐极小化子及其与相应的亚微分映射的伪度量次正则性的关系。