Modified Subgradient Extragradient Method for Pseudomonotone Variational Inequalities  

作　　者：Jiajia Cheng 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4期41-48,共8页哈尔滨工业大学学报（英文版）

摘　　要：Many approaches have been put forward to resolve the variational inequality problem. The subgradient extragradient method is one of the most effective. This paper proposes a modified subgradient extragradient method about classical variational inequality in a real Hilbert interspace. By analyzing the operator’s partial message, the proposed method designs a non-monotonic step length strategy which requires no line search and is independent of the value of Lipschitz constant, and is extended to solve the problem of pseudomonotone variational inequality. Meanwhile, the method requires merely one map value and a projective transformation to the practicable set at every iteration. In addition, without knowing the Lipschitz constant for interrelated mapping, weak convergence is given and R-linear convergence rate is established concerning algorithm. Several numerical results further illustrate that the method is superior to other algorithms.

关 键 词：variational inequality subgradient extragradient method non⁃monotonic stepsize strategy pseudomonotone mapping 

分 类 号：O221.2[理学—运筹学与控制论]