# Stability analysis for parameterized variational systems with implicit constraints

## TL;DR

This paper establishes new, weakly restrictive conditions for stability properties like isolated calmness and Aubin property in complex parameterized variational systems with implicit constraints, including quasi-variational inequalities.

## Contribution

It introduces novel stability conditions for variational systems with solution-dependent constraints using directional generalized differential calculus, applicable to broad classes of problems.

## Key findings

- Derived new conditions for isolated calmness.
- Established criteria for the Aubin property with parameter restrictions.
- Demonstrated applicability through academic examples.

## Abstract

In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems include, e.g., quasi-variational inequalities and implicit complementarity problems. Concerning the Aubin property, possible restrictions imposed on the parameter are also admitted. Throughout the paper, tools from the directional limiting generalized differential calculus are employed enabling us to impose only rather weak (non-restrictive) qualification conditions. Despite the very general problem setting, the resulting conditions are workable as documented by some academic examples