Generalized Metric Subregularity For Multifunction

Metric subregularity,as well as its related regularity properties such as error bound,weak sharp minima etc.,plays an important role in set-valued analysis,optimization theory and its applications.Due to its limitation in practical applica-tions,in recent years,many researchers considered generalized metric subregularity including ψ-metric subregularity,Holder metric subregularity and Pseudo metric subregularity etc.This thesis mainly focuses on studying generalized well-posedness property of generalized real-valued functions,generalized metric subregulaxity prop-erty of set-valued mappings as well as its perturbation analysis,which contains the following four aspects:In part 1,we mainly study generalized well-posedness property of generalized real-valued functions.Several primal and dual sufficient conditions for generalized well-posedness properties are established by virtue of descent direction in metric spaces and subdifferential in Banach space,respectively.In part 2,we mainly study ψ-metric subregularity as well as stability analysis of metric subregularity.Based on the results of generalized well-posedness,we first established several sufficient and necessary conditions for ψ-metric subregularity.Then,by the techniques of variational analysis,we provide sufficient conditions as well as characterizations for metric subregularity to be stable under the perturbation of a small Lipschitz continuous mapping.In part 3,we study Holder metric subregularity in a class of smooth spaces.Different from the existed results which,are expressed in terms of Clarke/Frechet subdifferential/normal cone etc.involving the " first-order "variational behavior,we provide dual sufficient conditions for Holder metric subregularity by virtue of prox-imal subdifferential,normal cone etc.which possess the "second-order" variational behavior.In part 4,we study Pseudo metric subregularity as well as its stability analysis in Asplund space.We first established several new dual sufficient conditions for Pseudo metric subregularity by virtue of Frechet subdifferential/normal cone.Then we provide characterizations for pseudo metric subregularity to be stable under the small perturbation of a p-order weak smooth mapping.