Stochastic Variational Inequality Approaches to the Stochastic Generalized Nash Equilibrium with Shared Constraints
Year: 2023
Author: Yanfang Zhang
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 3 : pp. 415–436
Abstract
In this paper, we consider the generalized Nash equilibrium with shared constraints in the stochastic environment, and we call it the stochastic generalized Nash equilibrium. The stochastic variational inequalities are employed to solve this kind of problems, and the expected residual minimization model and the conditional value-at-risk formulations defined by the residual function for the stochastic variational inequalities are discussed. We show the risk for different kinds of solutions for the stochastic generalized Nash equilibrium by the conditional value-at-risk formulations. The properties of the stochastic quadratic generalized Nash equilibrium are shown. The smoothing approximations for the expected residual minimization formulation and the conditional value-at-risk formulation are employed. Moreover, we establish the gradient consistency for the measurable smoothing functions and the integrable functions under some suitable conditions, and we also analyze the properties of the formulations. Numerical results for the applications arising from the electricity market model illustrate that the solutions for the stochastic generalized Nash equilibrium given by the ERM model have good properties, such as robustness, low risk and so on.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2109-m2020-0099
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 3 : pp. 415–436
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Stochastic generalized Nash equilibrium Stochastic variational inequalities Expected residual minimization model CVaR formulation Gradient consistency.