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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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Related citation:Yuwan Ding,Hongwei Liu,Xiaojun Ma.Inertial Subgradient Extragradient Algorithm for Solving Variational Inequality Problems with Pseudomonotonicity[J].Journal of Harbin Institute Of Technology(New Series),2023,30(5):65-75.DOI:10.11916/j.issn.1005-9113.2022049.
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Inertial Subgradient Extragradient Algorithm for Solving Variational Inequality Problems with Pseudomonotonicity
Author NameAffiliation
Yuwan Ding School of Mathematics and Statistics, Xidian University, Xi’an 710126, China 
Hongwei Liu School of Mathematics and Statistics, Xidian University, Xi’an 710126, China 
Xiaojun Ma School of Mathematics and Statistics, Xidian University, Xi’an 710126, China 
Abstract:
In order to solve variational inequality problems of pseudomonotonicity and Lipschitz continuity in Hilbert spaces, an inertial subgradient extragradient algorithm is proposed by virtue of non-monotone stepsizes . Moreover, weak convergence and R-linear convergence analyses of the algorithm are constructed under appropriate assumptions. Finally, the efficiency of the proposed algorithm is demonstrated through numerical implementations.
Key words:  variational inequality  extragradient method  pseudomonotonicity  Lipschitz continuity  weak and linear convergence
DOI：10.11916/j.issn.1005-9113.2022049
Clc Number:O224
Fund:
Descriptions in Chinese:
  

求解伪单调变分不等式的惯性次梯度外梯度算法

丁玉婉，刘红卫，马小军

（西安电子科技大学，数学与统计学院，西安 710126）

摘要：本文提出了一种利用非单调步长的惯性次梯度外梯度算法，用于求解 Hilbert 空间中具有伪单调性和利普希茨连续性的变分不等式问题。此外，在适当的条件下，给出了算法的弱收敛性和 R-线性收敛率。最后，通过数值实验验证了该算法的有效性。

关键词：变分不等式、外梯度算法、伪单调性、利普希茨连续、弱收敛和线性收敛

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