Radius Theorems for Subregularity in Infinite Dimensions

TL;DR

This paper extends and sharpens the theoretical understanding of the radius of subregularity in infinite-dimensional Banach and Asplund spaces, broadening the classes of perturbations for which robustness results hold.

Contribution

It generalizes previous results to more complex spaces and perturbation classes, improving the analytical tools for stability analysis of mathematical problems.

Findings

Extended radius of subregularity results to Banach/Asplund spaces

Sharpened coderivative tools for robustness analysis

Broadened classes of perturbations with valid radius formulas

Abstract

The paper continues our previous work [7] on the radius of subregularity that was initiated by Asen Dontchev. We extend the results of [7] to general Banach/Asplund spaces and to other classes of perturbations, and sharpen the coderivative tools used in the analysis of the robustness of well-posedness of mathematical problems and related regularity properties of mappings involved in the statements. We also expand the selection of classes of perturbations, for which the formula for the radius of strong subregularity is valid.