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

Zhen Ping Yang, Yuliang WANG, Gui Hua Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number2050011
JournalAsia-Pacific Journal of Operational Research
Volume37
Issue number3
DOIs
Publication statusPublished - 1 Jun 2020

Scopus Subject Areas

  • Management Science and Operations Research

User-Defined Keywords

  • linear convergence rate
  • modified backward-forward algorithm
  • stochastic approximation
  • stochastic natural gas trading market
  • Stochastic variational inequality

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