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Supervised by Ministry of Industry and Information Technology of The People's Republic of China Sponsored by Harbin Institute of Technology Editor-in-chief Yu Zhou ISSNISSN 1005-9113 CNCN 23-1378/T

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Weak and strong convergence of self adaptive inertial subgradient extragradient algorithms for solving variational inequality problems
Author NameAffiliationPostcode
Yao Li* School of Mathematics and Statistics, Xidian University, Xi''an, 710126, China 710126
Hongwei Liu School of Mathematics and Statistics, Xidian University, Xi''an, 710126, China 710126
Jiamin Lv School of Mathematics and Statistics, Xidian University, Xi''an, 710126, China 710126
Abstract:
Many solutions of variational inequalities have been proposed, among which the subgradient extragradient method has obvious advantages. Two different algorithms are given for solving variational inequality problem in this paper. The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition. Two new algorithms adopt inertial technology and non-monotonic step size rule, and their convergence can still be proved when the value of L is not given in advance.Finally, some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.
Key words:  variational inequality  inertial method  non-monotonic step size rule  Lipschitz continuity  pseudomonotone mapping
DOI：10.11916/j.issn.1005-9113.2023028
Clc Number:O224
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