Variable sample-size optimistic mirror descent algorithm for stochastic mixed variational inequalities

In this paper, we propose a variable sample-size optimistic mirror descent algorithm under the Bregman distance for a class of stochastic mixed variational inequalities. Different from those conventional variable sample-size extragradient algorithms to evaluate the expected mapping twice at each ite...

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Bibliographic Details
Published in:Journal of global optimization Vol. 89; no. 1; pp. 143 - 170
Main Authors: Yang, Zhen-Ping, Zhao, Yong, Lin, Gui-Hua
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2024
Springer
Springer Nature B.V
Subjects:
Algorithms
Approximation
Computer Science
Convergence
Inequalities
Mapping
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Mirror descent
Stochastic mixed variational inequality
90C33
Convergence rate
90C15
Bregman distance
Local stability
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, we propose a variable sample-size optimistic mirror descent algorithm under the Bregman distance for a class of stochastic mixed variational inequalities. Different from those conventional variable sample-size extragradient algorithms to evaluate the expected mapping twice at each iteration, our algorithm requires only one evaluation of the expected mapping and hence can significantly reduce the computation load. In the monotone case, the proposed algorithm can achieve O ( 1 / t ) ergodic convergence rate in terms of the expected restricted gap function and, under the strongly generalized monotonicity condition, the proposed algorithm has a locally linear convergence rate of the Bregman distance between iterations and solutions when the sample size increases geometrically. Furthermore, we derive some results on stochastic local stability under the generalized monotonicity condition. Numerical experiments indicate that the proposed algorithm compares favorably with some existing methods.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-023-01346-0