Pseudo metric subregularity and its stability in Asplund spaces
Pseudo metric subregularity and its stability in Asplund spaces
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Asplund 空间中的伪度量次正则性及其稳定性
DOI：
10.1007/s11117-020-00772-8
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发表时间：
2021
期刊：
影响因子：
1
通讯作者：
Zhu Jiangxing
中科院分区：
文献类型：
--
作者：
Zhang Binbin;Zhu Jiangxing
作为度量次正则性的一个变种，伪度量次正则性是通过广义极限临界集的变分分析方法来研究的。利用极限临界集，给出了伪/Hölder度量次正则性成立的充分条件.通常，伪度量次正则性在小的光滑扰动下是不稳定的。给出了伪度量次正则性在小光滑扰动下稳定的一个刻划.特别地，将已有的度量次正则性的结果推广到伪度量次正则性。最后，讨论了真下连续函数的伪弱sharp极小元及其与相应次微分映射的伪度量次正则性的关系。
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 smallsmooth 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.