Hilbert空间中求解伪单调变分不等式的自适应次梯度外梯度法  

The Self Adaptive Subgradient Extragradient Method for Solving Pseudomonotone Variational Inequality Problems in Hilbert Spaces

作　　者：谢忠兵 蔡钢 李肖肖 董巧丽[2] Zhong Bing XIE;Gang CAI;Xiao Xiao LI;Qiao Li DONG(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China;College of Science,Civil Aviation University of China,Tianjin 300300,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]中国民航大学理学院,天津300300

出　　处：《数学学报（中文版）》2023年第4期693-706,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12171062);重庆市自然科学基金(cstc2020jcyj-msxmX0455);重庆市教委项目(KJZD-K201900504);重庆市研究生科研创新项目(CYS21269)。

摘　　要：本文在实Hilbert空间上研究一种关于伪单调变分不等式的新算法.该算法结合次梯度外梯度法、惯性法和黏性法.在适当的条件下,引入不同的参数来改进算法的收敛性.最后,在数值试验中与相关结果作比较,展示所提算法的有效性.We study a new iterative algorithm for solving pseudomonotone variational inequality problems in real Hilbert spaces.The proposed algorithm combines the subgradient extragradient method,the inertial method and the viscosity method.Under appropriate conditions imposed on the parameters,we accelerate and improve the convergence of the algorithm by introducing different parameters.Finally,some numerical experiments are proposed to show the efficiency of our algorithm through comparison with related algorithms.

关 键 词：强收敛 次梯度外梯度法 惯性法 黏性法 变分不等式 

分 类 号：O177.91[理学—数学]