An inertial subgradient extragradient algorithm with adaptive stepsizes for variational inequality problems

In this paper, we introduce an efficient subgradient extragradient (SE) based method for solving variational inequality problems with monotone operator in Hilbert space. In many existing SE methods, two values of operator are needed over each iteration and the Lipschitz constant of the operator or l...

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Bibliographic Details
Published in:Optimization methods & software Vol. 37; no. 4; pp. 1507 - 1526
Main Authors: Chang, Xiaokai, Liu, Sanyang, Deng, Zhao, Li, Suoping
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.07.2022
Taylor & Francis Ltd
Subjects:
Adaptive algorithms
adaptive step size
Hilbert space
inertial method
Iterative methods
locally Lipschitz continuous
Mathematical analysis
subgradient extragradient method
Variational inequalities
ISSN:1055-6788, 1029-4937
Online Access:Get full text
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Summary:In this paper, we introduce an efficient subgradient extragradient (SE) based method for solving variational inequality problems with monotone operator in Hilbert space. In many existing SE methods, two values of operator are needed over each iteration and the Lipschitz constant of the operator or linesearch is required for estimating step sizes, which are usually not practical and expensive. To overcome these drawbacks, we present an inertial SE based algorithm with adaptive step sizes, estimated by using an approximation of the local Lipschitz constant without running a linesearch. Each iteration of the method only requires a projection on the feasible set and a value of the operator. The numerical experiments illustrate the efficiency of the proposed algorithm.
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ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2021.1910946