A strong metric subregularity analysis of nonsmooth mappings via steepest displacement rate

TL;DR

This paper introduces a variational approach using the steepest displacement rate to analyze strong metric subregularity of nonsmooth mappings, providing new criteria for stability and detection.

Contribution

It offers a novel characterization of strong metric subregularity for multifunctions in metric spaces using the steepest displacement rate, enhancing analysis of nonsmooth mappings.

Findings

Characterization of strong metric subregularity via steepest displacement rate

Stability criteria for perturbations affecting subregularity

Conditions for detecting subregularity in nonsmooth mappings

Abstract

In this paper, a systematic study of the strong metric subregularity property of mappings is carried out by means of a variational tool, called steepest displacement rate. With the aid of this tool, a simple characterization of strong metric subregularity for multifunctions acting in metric spaces is formulated. The resulting criterion is shown to be useful for establishing stability properties of the strong metric subregularity in the presence of perturbations, as well as for deriving various conditions, enabling to detect such a property in the case of nonsmooth mappings. Some of these conditions, involving several nonsmooth analysis constructions, are then applied in studying the isolated calmness property of the solution mapping to parameterized generalized equations.