Generalized Metric Subregularity and Regularity with Respect to an Admissible Function
本文引入一种关于容许函数的广义度量次正则性/正则性概念，它是Hölder度量正则性的自然推广，并利用余导数给出了多值函数满足该性质的充分条件，特别推广了度量正则性和Hölder度量正则性的已有结果。
In this paper, adopting an admissible function $\varphi$, we consider a kind of generalized metric subregularity/regularity of a multifunction $F$ with respect to $\varphi$, which is a natural generalization of the Hölder metric regularity. In the special case when $F$ is the subdifferential mapping of a proper lower semicontinuous function $f$, it is known that such a generalized metric subregularity is very closely related to the well-posedness of $f$. Using the technique of variational analysis and in terms of the coderivative, we established some sufficient conditions for a multifunction to be metrically subregular/regular with respect to an admissible function $\varphi$. In particular, we extend some existing results on the metric regularity and Hölder metric regularity.