Error Bounds and Metric Subregularity

TL;DR

This paper develops criteria for metric subregularity of set-valued mappings using error bounds and subdifferential slopes, providing a unified classification framework applicable in metric and Banach spaces.

Contribution

It introduces necessary and sufficient conditions for metric subregularity based on error bounds and subdifferential slopes, advancing the theoretical understanding of set-valued mappings.

Findings

Provides a classification scheme for error bounds and metric subregularity criteria.

Formulates criteria using primal and subdifferential slopes.

Establishes a unified approach applicable in general metric and Banach spaces.

Abstract

Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued functions of two variables. A classification scheme for the general error bound and metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes.