On the Aubin property of a class of parameterized variational systems

TL;DR

This paper introduces a new sharp criterion for the Aubin property of solution maps in parameterized variational systems, extending calculus tools for non-polyhedral and conic constraints, with practical examples.

Contribution

It provides a novel second-order chain rule-based criterion for the Aubin property applicable to complex variational systems with non-polyhedral and conic constraints.

Findings

New criterion for Aubin property established

Formulas extend existing calculus of directional limiting objects

Illustrated with practical examples

Abstract

The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets and also parameterized generalized equations with conic constraints. The new criterion requires computation of directional limiting coderivatives of the normal-cone mapping for the so-called critical directions. The respective formulas have the form of a second-order chain rule and extend the available calculus of directional limiting objects. The suggested procedure is illustrated by means of examples.