A survey on the metric regularity and applications
The theory of metric regularity and related topics plays an important role in variational analysis and have many applications in optimization. In recent decades, it has attracted the study of many researchers in both the theoretical aspects and applications. In the survey paper, we present some recent developments, with emphasis on the results established by our research group in the recent decade in this theory and its applications in the study of the Newton-type methods for solving generalized equations. In addition, based on the metric regularity, we establish a new result on a generalization of the convex principle for paraconvex multimaps.