Regularized Sample Average Approximation Approach for Two-Stage Stochastic Variational Inequalities

Jie Jiang () and Shengjie Li ()
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Jie Jiang: Chongqing University
Shengjie Li: Chongqing University

Journal of Optimization Theory and Applications, 2021, vol. 190, issue 2, No 13, 650-671

Abstract: Abstract Sample average approximation (SAA) approach for two-stage stochastic variational inequalities (SVIs) with continuous probability distributions, where the second-stage problems have multiple solutions, may not promise convergence assertions as the sample size tends to infinity. In this paper, a regularized SAA approach is proposed to numerically solve a class of two-stage SVIs with continuous probability distributions, where the second-stage problems are monotone and allowed to have multiple solutions. We first give some structural properties. After that, the convergence analysis of the regularized SAA approach for two-stage SVIs is investigated as the regularization parameter tends to zero and the sample size tends to infinity. Finally, we employ the progressive hedging algorithm to report some numerical results.

Keywords: Two-stage; Stochastic variational inequality; SAA; Regularization method; Convergence analysis; 90C15; 90C33; 49J53 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-021-01905-z

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