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Variance-Based Modified Backward-Forward Algorithm with Line Search for Stochastic Variational Inequality Problems and Its Applications

Author

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  • Zhen-Ping Yang

    (School of Management, Shanghai University, Shanghai 200444, P. R. China)

  • Yuliang Wang

    (Department of Mathematics, Hong Kong Baptist University, Hong Kong 999077, P. R. China3HKBU Institute of Research and Continuing Education, Shenzhen 518000, P. R. China)

  • Gui-Hua Lin

    (School of Management, Shanghai University, Shanghai 200444, P. R. China)

Abstract

We propose a variance-based modified backward-forward algorithm with a stochastic approximation version of Armijo’s line search, which is robust with respect to an unknown Lipschitz constant, for solving a class of stochastic variational inequality problems. A salient feature of the proposed algorithm is to compute only one projection and two independent queries of a stochastic oracle at each iteration. We analyze the proposed algorithm for its asymptotic convergence, sublinear convergence rate in terms of the mean natural residual function, and optimal oracle complexity under moderate conditions. We also discuss the linear convergence rate with finite computational budget for the proposed algorithm without strong monotonicity. Preliminary numerical experiments indicate that the proposed algorithm is competitive with some existing algorithms. Furthermore, we consider an application in dealing with an equilibrium problem in stochastic natural gas trading market.

Suggested Citation

  • Zhen-Ping Yang & Yuliang Wang & Gui-Hua Lin, 2020. "Variance-Based Modified Backward-Forward Algorithm with Line Search for Stochastic Variational Inequality Problems and Its Applications," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(03), pages 1-33, April.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:03:n:s0217595920500116
    DOI: 10.1142/S0217595920500116
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    Cited by:

    1. Zhen-Ping Yang & Gui-Hua Lin, 2021. "Variance-Based Single-Call Proximal Extragradient Algorithms for Stochastic Mixed Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 393-427, August.

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