On the Aubin property of solution maps to parameterized variational systems with implicit constraints

TL;DR

This paper introduces a new sufficient condition for the Aubin property of solution maps in parameterized variational systems with implicit constraints, applicable to complex systems like quasi-variational inequalities.

Contribution

It develops a verifiable criterion for the Aubin property using directional limiting coderivatives, applicable without explicit coderivative computation.

Findings

New sufficient condition for Aubin property derived

Applicable to systems with parameter-dependent and implicit constraints

Condition verified through an illustrative example

Abstract

In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they include, e.g., parameter-dependent quasi-variational inequalities and implicit complementarity problems. The result is based on a general condition ensuring the Aubin property of implicitly defined multifunctions which employs the recently introduced notion of the directional limiting coderivative. Our final condition can be verified, however, without an explicit computation of these coderivatives. The procedure is illustrated by an example.