Sensitivity Analysis of Stochastic Constraint and Variational Systems via Generalized Differentiation

TL;DR

This paper develops methods for analyzing the stability of stochastic constraint and variational systems, providing conditions for robustness and new ways to compute derivatives in stochastic optimization contexts.

Contribution

It introduces generalized differentiation techniques to characterize well-posedness and stability of stochastic systems, advancing the theoretical understanding and computational tools in stochastic variational analysis.

Findings

Established conditions for Lipschitzian stability and metric regularity.

Developed coderivative characterizations for random multifunctions.

Provided efficient evaluation methods for coderivatives in stochastic models.

Abstract

This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian stability and/or metric regularity, of such systems by employing and developing coderivative characterizations of well-posedness properties for random multifunctions and efficiently evaluating coderivatives of special classes of random integral set-valued mappings that naturally emerge in stochastic programming and stochastic variational inequalities.