Variance-Based Subgradient Extragradient Method for Stochastic Variational Inequality Problems

In this paper, we propose a variance-based subgradient extragradient algorithm with line search for stochastic variational inequality problems by aiming at robustness with respect to an unknown Lipschitz constant. This algorithm may be regarded as an integration of a subgradient extragradient algori...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 89; no. 1; p. 4
Main Authors: Yang, Zhen-Ping, Zhang, Jin, Wang, Yuliang, Lin, Gui-Hua
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2021
Springer Nature B.V
Subjects:
Algebra
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Convergence
Iterative methods
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Numerical analysis
Random variables
Regularization methods
Robustness (mathematics)
Theoretical
Stochastic variational inequality
65K15
Bounded proximal error bound
90C33
Variance reduction
Convergence rate
Stochastic approximation
90C15
Subgradient extragradient algorithm
62L20
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:In this paper, we propose a variance-based subgradient extragradient algorithm with line search for stochastic variational inequality problems by aiming at robustness with respect to an unknown Lipschitz constant. This algorithm may be regarded as an integration of a subgradient extragradient algorithm for deterministic variational inequality problems and a stochastic approximation method for expected values. At each iteration, different from the conventional variance-based extragradient algorithms to take projection onto the feasible set twicely, our algorithm conducts a subgradient projection which can be calculated explicitly. Since our algorithm requires only one projection at each iteration, the computation load may be reduced. We discuss the asymptotic convergence, the sublinear convergence rate in terms of the mean natural residual function, and the optimal oracle complexity for the proposed algorithm. Furthermore, we establish the linear convergence rate with finite computational budget under both the strongly Minty variational inequality and the error bound condition. Preliminary numerical experiments indicate that the proposed algorithm is competitive with some existing methods.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-021-01603-y