Hilbert空间上变分不等式问题的外梯度算法  

An Extragradient Algorithm for Variational Inequality Problems in Hilbert Spaces

作　　者：胡绍涛 王元恒 蔡钢 Shao Tao HU;Yuan Heng WANG;Gang CAI(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,P.R.China;School of Mathematical Sciences,Chongqing Normal University,Chongqing401331,P.R.China)

机构地区：[1]浙江师范大学数学与计算机科学学院,金华321004 [2]重庆师范大学数学科学学院,重庆401331

出　　处：《数学学报（中文版）》2023年第5期845-854,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12171435,12171062)。

摘　　要：本文在Hilbert空间上提出一种关于伪单调变分不等式问题的新Tseng外梯度算法.我们证明由算法生成的序列强收敛到变分不等式解集的一个元素.所得结果推广和改进了很多最新结果.We introduce a new Tseng's extragradient algorithm for solving pseu-domonotone variational inequality problems in Hilbert spaces.We prove that the sequence generated by our proposed algorithm converges strongly to an element of solution set for variational inequality problems.The results obtained in this paper extend and improve many recent ones in the literature.

关 键 词：强收敛 Tseng外梯度算法 变分不等式 HILBERT空间 伪单调算子 

分 类 号：O177.91[理学—数学]