Directional Metric Subregularity Of A Subsmooth Set-valued Mappings

The idea and method of metric subregularity have penetrated into many fields of mathematics,such as optimization problems,error analysis and so on.Therefore,scholars have done a lot of work on the research of metric subregularity.Zheng and Ng characterize their metric subregularity with the help of Clarke coderivative of set-valued mappings.On some problems,we need to consider that the metric subregularity of setvalued mappings in a certain direction is established,Inspired by the research ideas of Zheng and Ng,,in this thesis we study the directional metric subregularity of a class of subsmooth set-valued mappings with the help of the tool of mordukhovich coderivative of set-valued mappings,and obtains some sufficient conditions for the directional metric subregularity of set-valued mappings.