Distributionally Robust Variational Inequalities: Relaxation, Quantification and Discretization

Jie Jiang ()
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Jie Jiang: Chongqing University

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 10, 227-255

Abstract: Abstract In this paper, we use the distributionally robust approach to study stochastic variational inequalities under the ambiguity of the true probability distribution, which is referred to as distributionally robust variational inequalities (DRVIs). First of all, we adopt a relaxed value function approach to relax the DRVI and obtain its relaxation counterpart. This is mainly motivated by the robust requirement in the modeling process as well as the possible calculation error in the numerical process. After that, we investigate qualitative convergence properties as the relaxation parameter tends to zero. Considering the perturbation of ambiguity sets, we further study the quantitative stability of the relaxation DRVI. Finally, when the ambiguity set is given by the general moment information, the discrete approximation of the relaxation DRVI is discussed.

Keywords: Stochastic variational inequality; Distributional robustness; Quantitative stability; Discretization; Rate of convergence; 90C15; 90C33 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02497-0

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