Dynamic stochastic projection method for multistage stochastic variational inequalities

Bin Zhou, Jie Jiang and Hailin Sun ()
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Bin Zhou: Nanjing Normal University
Jie Jiang: Chongqing University
Hailin Sun: Nanjing Normal University

Computational Optimization and Applications, 2024, vol. 89, issue 2, No 7, 485-516

Abstract: Abstract Stochastic approximation (SA) type methods have been well studied for solving single-stage stochastic variational inequalities (SVIs). This paper proposes a dynamic stochastic projection method (DSPM) for solving multistage SVIs. In particular, we investigate an inexact single-stage SVI and present an inexact stochastic projection method (ISPM) for solving it. Then we give the DSPM to a three-stage SVI by applying the ISPM to each stage. We show that the DSPM can achieve an $$\mathcal {O}(\frac{1}{\epsilon ^2})$$ O ( 1 ϵ 2 ) convergence rate regarding to the total number of required scenarios for the three-stage SVI. We also extend the DSPM to the multistage SVI when the number of stages is larger than three. The numerical experiments illustrate the effectiveness and efficiency of the DSPM.

Keywords: Multistage stochastic variational inequalities; Stochastic approximation method; Inexact stochastic projection method; Dynamic stochastic projection method; Convergence rate (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00594-4

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