On computation of limiting coderivatives of the normal-cone mapping to inequality systems and their applications

TL;DR

This paper develops methods to compute the limiting coderivative of the normal-cone mapping for inequality constraints under weak conditions, and applies these results to verify the Aubin property of solution maps in generalized equations.

Contribution

It introduces new techniques for calculating limiting coderivatives of the normal-cone mapping under minimal qualification assumptions.

Findings

Derived explicit formulas for limiting coderivatives

Verified the Aubin property for certain solution maps

Extended applicability to weak qualification conditions

Abstract

The paper concerns the computation of the limiting coderivative of the normal-cone mapping related to $C^{2}$ inequality constraints under weak qualification conditions. The obtained results are applied to verify the Aubin property of solution maps to a class of parameterized generalized equations.