Asplund空间中随机集值隐函数的度量正则性

Metric Regularity of Random Implicit Multifunctions in Asplund Spaces

在Asplund空间中讨论随机集值隐函数的度量正则性,所使用的工具有Ekeland变分原理、Fermat原理、Lipschitz函数的次微分以及次梯度的加法原理等.首先,给出随机集值隐函数的局部度量正则性成立的充分条件.其次,利用上述结果,分别给出随机集值隐函数的度量正则性和Lipschitz性质成立的充分条件.所得结果改进了已有文献中的相关结果.

This paper is mainly devoted to the discussion of metric regularity of random implicit multifunctions in Asplund spaces with the Ekeland variational principle,the Fermat rule,subdifferentials of Lipschitzian functions and sum rules for basic and singular subgradients.Firstly,the new sufficient conditions for the local metric regularity of random implicit multifunctions are given.Secondly,by using the above result,sufficient conditions for the metric regularity and the Lipschitz property of random implicit multifunctions are given in Asplund spaces.These results improve the corresponding results known in literature.