Robinson Stability of Parametric Constraint Systems via Variational Analysis

TL;DR

This paper explores Robinson stability in parametric constraint systems using variational analysis, providing new conditions and relationships with other stability properties, and applying findings to robust Lipschitzian stability.

Contribution

It introduces first- and second-order conditions for Robinson stability under minimal assumptions, advancing the theoretical understanding of well-posedness in variational systems.

Findings

Derived first- and second-order conditions for Robinson stability.

Established relationships between Robinson stability and other well-posedness properties.

Applied results to robust Lipschitzian stability of variational systems.

Abstract

This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order conditions for this property under minimal constraint qualifications and establish relationships of Robinson stability with other well-posedness properties in variational analysis and optimization. The results obtained are applied to robust Lipschitzian stability of parametric variational systems.