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

Zhen-Ping Yang (), Yuliang Wang and Gui-Hua Lin
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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

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 03, 1-33

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.

Keywords: Stochastic variational inequality; stochastic approximation; modified backward-forward algorithm; linear convergence rate; stochastic natural gas trading market (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0217595920500116

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