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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:Lulu Yin,Hongwei Liu.Subgradient Extragradient Methods for Equilibrium Problems and Fixed Point Problems in Hilbert Space[J].Journal of Harbin Institute Of Technology(New Series),2022,29(1):15-23.DOI:10.11916/j.issn.1005-9113.2020029.
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Subgradient Extragradient Methods for Equilibrium Problems and Fixed Point Problems in Hilbert Space
Author NameAffiliation
Lulu Yin School of Mathematics and Statistics, Xidian University, Xi′an 710126, China 
Hongwei Liu School of Mathematics and Statistics, Xidian University, Xi′an 710126, China 
Abstract:
Inspired by inertial methods and extragradient algorithms, two algorithms were proposed to investigate fixed point problem of quasinonexpansive mapping and pseudomonotone equilibrium problem in this study. In order to enhance the speed of the convergence and reduce computational cost, the algorithms used a new step size and a cutting hyperplane. The first algorithm was proved to be weak convergence, while the second algorithm used a modified version of Halpern iteration to obtain strong convergence. Finally, numerical experiments on several specific problems and comparisons with other algorithms verified the superiority of the proposed algorithms.
Key words:  subgradient extragradient methods  inertial methods  pseudomonotone equilibrium problems  fixed point problems  Lipschitz-type condition
DOI：10.11916/j.issn.1005-9113.2020029
Clc Number:O224
Fund:
Descriptions in Chinese:
  

Hilbert空间中平衡问题和不动点问题的次梯度外梯度方法

尹璐璐,刘红卫

（西安电子科技大学 数学与统计学院，西安 710126）

中文说明：

基于惯性方法和次梯度外梯度方法，本文提出求解拟非扩张的不动点问题和伪单调平衡问题公共解的两种算法。为了提高收敛速度，减少计算量，证明第一种算法是弱收敛的，而第二种算法使用了改进版的 Halpern 迭代来获得强收敛性。最后通过几个具体问题的数值实验以及与其他算法的对比验证了所提算法的优越性。

关键词：次梯度外梯度方法；惯性方法；伪单调平衡问题；不动点问题；Lipschitz型条件

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