Perturbation Analysis Of Error Bounds For A Class Of Multifunctions

The stability of error bounds is of great significance in optimization theory.Recently,Zheng and Ng [40] studied the stability of the error bounds of the system of conic quasi-subsmooth inequalities under the assumption that the ordering cone has non-empty interior by using the coderivatives of vector-valued functions.Motivated by the papers of Zheng and Ng [40],Hu and He [11] studied the stability of error bounds for single-valued mappings under the weaker assumption that the ordering cone is dually compact.By means of the coderivatives of the vector-valued functions,the lower bound of the perturbation radius of the error bounds is estimated and the sufficient condition for the stability of the error bounds is given.Based on the results of Zheng and Ng [40] as well as Hu and He [11],we consider the perturbation problem of error bounds for weakly quasisubsmooth multi-valued mappings under the assumption that the ordering cone is dually compact.In this thesis,we introduce the concept of weakly quasi-subsmooth multi-valued mappings,define the radius of error bounds of this kind of multi-valued mappings,and obtain some sufficient conditions for the stability of the error bounds of this kind of multivalued mappings under the condition that the ordering cone is dually compact.We extend the relevant results of Zheng and Ng as well as Hu and He on single-valued mappings to more general cases.