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.
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Acknowledgements
The authors are very grateful to two anonymous referees whose constructive suggestions and remarks allowed us to essentially improve the original presentation.
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Research of the first author was partly supported by the USA National Science Foundation under grant DMS-1808978, by the Australian Research Council under Discovery Project DP-190100555, and by the Project 111 of China under grant D21024. Research of the second author was partly supported by the Chilean grants: Fondecyt Regular 1190110 and Fondecyt Regular 1200283.
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Mordukhovich, B.S., Pérez-Aros, P. Sensitivity Analysis of Stochastic Constraint and Variational Systems via Generalized Differentiation. Set-Valued Var. Anal 31, 4 (2023). https://doi.org/10.1007/s11228-023-00660-9
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DOI: https://doi.org/10.1007/s11228-023-00660-9
Keywords
- Variational analysis
- Set-valued analysis
- Lipschitzian stability
- Generalized differentiation
- Coderivatives
- Stochastic programming
- Stochastic variational inequalities