Two fast variance-reduced proximal gradient algorithms for SMVIPs-Stochastic Mixed Variational Inequality Problems with suitable applications to stochastic network games and traffic assignment problems

In this paper, we propose two proximal gradient algorithms with variance reduction for stochastic mixed variational inequality problems. One is a proximal extragradient algorithm and another is a proximal forward–backward–forward algorithm. Under the monotonicity assumption on the mapping F and othe...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 408; p. 114132
Main Authors: Yang, Zhen-Ping, Lin, Gui-Hua
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2022
Subjects:
Complexity
Nonlinear programming
Proximal algorithm
Stochastic approximation
Stochastic mixed variational inequality
Variance reduction
Stochastic mixed variational inequality
90C33
Proximal algorithm
Variance reduction
Stochastic approximation
90C15
Nonlinear programming
Complexity
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:In this paper, we propose two proximal gradient algorithms with variance reduction for stochastic mixed variational inequality problems. One is a proximal extragradient algorithm and another is a proximal forward–backward–forward algorithm. Under the monotonicity assumption on the mapping F and other moderate conditions, we derive some asymptotic convergence properties and O(1/k) convergence rate in terms of the restricted gap function values for the proposed algorithms. Furthermore, under the bounded metric subregularity condition, we investigate the linear convergence rate and oracle complexity bounds for the proposed algorithms when the sample-size increases at a geometric rate. If the sample-size increases at a polynomial rate of ⌈k+1⌉−s with s>0, the mean-squared distance of the iterates to the solution set decays at a corresponding polynomial rate, while the iterations and oracle complexities to obtain an ε-solution are O(1/ε1/s) and O(1/ε1+1/s) respectively. Finally, some numerical experiments on stochastic network games and traffic assignment problems indicate that the proposed algorithms are efficient. •We study a class of stochastic mixed variational inequality problems.•We present two variance-based proximal algorithms for the considered problem.•We establish asymptotic convergence and oracle complexity of the proposed algorithms.•We carry out numerical experiments on network games and traffic assignment problems.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114132