Metric Subregularity Of A Class Of Set-valued Mappings

Metric subregularity of a set-valued mapping plays an important role in optimization,especially as the constraint condition of optimality condition.By adopting the methods of variational analysis and subdifferential,and using tangent cones,normal cones and coderivative as tools,this thesis analyses the metric subregularity of a set-valued mapping in finite dimensional Hilbert space,which is the sum of a continuous differentiable single valued mapping and a continuous closed convex set-valued mapping.Firstly,a sufficient condition is obtained for the strong metric subregularity of this kind of set-valued mappings under the appropriate continuity assumption;then,the thesis explores the direction metric subregularity of this type of setvalued mappings under the condition of some “single value selection”,and some sufficient conditions are proposed for the direction metric subregularity of this kind of set-valued mappings.