Error Bounds and Holder Metric Subregularity

TL;DR

This paper investigates the Holder metric subregularity of set-valued mappings using error bounds and subdifferential slopes, providing a classification scheme for criteria in general metric and Banach spaces.

Contribution

It introduces a classification scheme for Holder metric subregularity criteria based on primal and subdifferential slopes in a broad functional analysis setting.

Findings

Classification scheme for Holder subregularity criteria

Criteria formulated using primal and subdifferential slopes

Applicable to general metric and Banach/Asplund spaces

Abstract

The Holder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extended real-valued functions of two variables. A classification scheme for the general Holder metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes.