Characterizations of the Aubin property of the KKT-mapping in composite optimization by SC derivatives and quadratic bundles

TL;DR

This paper characterizes the Aubin property of the KKT-mapping in composite optimization using SC derivatives and quadratic bundles, providing more accessible tools than traditional coderivatives.

Contribution

It introduces new characterizations of the Aubin property and Lipschitzian localizations for the KKT-mapping via SC derivatives and quadratic bundles, simplifying analysis.

Findings

Aubin property characterized by SC derivatives.

Existence of Lipschitzian localizations linked to quadratic bundles.

Simplifies the analysis of KKT-mapping properties.

Abstract

For general set-valued mappings, the Aubin property is ultimately tied to limiting coderivatives by the Mordukhovich criterion. Likewise, the existence of single-valued Lipschitzian localizations is related to strict graphical derivatives. In this paper we will show that for the special case of the KKT-mapping from composite optimization, the Aubin property and the existence of single-valued Lipschitzian localizations can be characterized by SC derivatives and quadratic bundles, respectively, which are easier accessible than limiting coderivatives and strict graphical derivatives.