Nonlinear Metric Subregularity

TL;DR

This paper explores nonlinear metric subregularity of set-valued mappings in metric and Banach spaces, linking it to error bounds theory and establishing criteria and relationships between different subregularity conditions.

Contribution

It extends the theory of error bounds to nonlinear metric subregularity, providing new criteria and relationships in general metric and Banach spaces.

Findings

Formulated primal and dual criteria for nonlinear metric subregularity.

Established relationships between different criteria of subregularity.

Illustrated criteria with examples and theoretical analysis.

Abstract

In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error bounds for extended real-valued functions of two variables developed in A. Y. Kruger, Error bounds and metric subregularity, Optimization 64, 1 (2015) 49-79. Several primal and dual space local quantitative and qualitative criteria of nonlinear metric subregularity are formulated. The relationships between the criteria are established and illustrated.