Directional Metric Subregularity For Multifunctions And Applications

The constraint qualifications play an important role in optimality conditions for optimization problems and some certain constraint qualifications mean the regularity of mappings.Thus,it is necessary to study the regularity of a mapping.In this thesis,the direction metric subregularity of multifunctions and its application in optimization are studied.Firstly,the concepts of directional metric subregularity and directional calmness are defined.We obtain a linear characterization of directional metric subregularity.Further,it is proved that the direction metric subregularity has directional linear openness.Then,the duality of directional calmness is studied and a necessary condition of directional calmness is obtained.The necessary and sufficient conditions of direction metric subregularity are obtained by means of subdifferential,(generalized)Ekeland variational principle and so on.Finally,the definitions of direction openness and direction strong metric subregularity of a multifunction are given,prove that between local Pareto maximum points and directional openness have certain incompatibility,so the necessary and sufficient conditions for vector optimization problem of multifunctions are obtained.