Full stability of general parametric variational systems

TL;DR

This paper characterizes and provides verifiable conditions for full stability of solutions in parametric variational systems with nonsmooth data, using second-order variational analysis in Hilbert spaces.

Contribution

It introduces and fully characterizes Lipschitzian and H"olderian full stability for parametric variational systems with nonsmooth mappings, including explicit formulas and estimates.

Findings

Complete characterizations of full stability notions.

Verifiable sufficient conditions established.

Explicit formulas and quantitative estimates derived.

Abstract

The paper introduces and studies the notions of Lipschitzian and H\"olderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial subgradients of prox-regular functions acting in Hilbert spaces. Employing advanced tools and techniques of second-order variational analysis allows us to establish complete characterizations of, as well as directly verifiable sufficient conditions for, such full stability notions under mild assumptions. Furthermore, we derive exact formulas and effective quantitative estimates for the corresponding moduli. The obtained results are specified for important classes of variational inequalities and variational conditions in both finite and infinite dimensions.