Subgradient Extragradient Methods for Equilibrium Problems and Fixed Point Problems in Hilbert Space  

作　　者：Lulu Yin Hongwei Liu 

机构地区：[1]School of Mathematics and Statistics,Xidian University,Xi′an 710126,China

出　　处：《Journal of Harbin Institute of Technology(New Series)》2022年第1期15-23,共9页哈尔滨工业大学学报（英文版）

摘　　要：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.

关 键 词：subgradient extragradient methods inertial methods pseudomonotone equilibrium problems fixed point problems Lipschitz⁃type condition 

分 类 号：O224[理学—运筹学与控制论]