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

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.

💡 Research Summary

The paper investigates stability properties of the Karush‑Kuhn‑Tucker (KKT) mapping arising from a broad class of composite optimization problems of the form
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