四川师范大学学报（自然科学版）2011，Vol.34Issue(5)：605-609,5.DOI:10.3969/j.issn.1001-8395.2011.05.002
改进的超梯度算法在无穷维Hilbert空间强收敛
Strong Convergence of Modified Extragradient Method in Infinite Hilbert Space
摘要
Abstract
Many methods have been proposed to solve Ⅵ(F,X). The simplest is the extragradient method which was proposed by G. M. Korpelevich( Matecon, 1976,12:747 -756. ). This method was modified by many scholars. Among all the algorithms, the method of paper (Y. J. Wang, N. H. Xiu, J. Z. Zhang. J Optim Theory Appl,2003,119:167 - 168. ) can use the convergence property of the generated sequences to verify the existence of solution without assuming the existence of the solution. This paper extends the midified extragradient method which was proposed by Y. J. Wang, N. H. Xiu and J. Z. Zhang to infinite-dimensional Hilbert space and discusses convergence properties of modified extragradient algorithm for pseudomonotone variational inequality in an infinite-dimensional Hilbert space.关键词
超梯度算法/Hilbert空间:弱收敛/强收敛:伪单调Key words
extragradient method/ Hilbert space/ weak convergence/ strong convergence/ pseudomonotone分类
数理科学引用本文复制引用
晏萍,何诣然..改进的超梯度算法在无穷维Hilbert空间强收敛[J].四川师范大学学报（自然科学版）,2011,34(5):605-609,5.基金项目
国家自然科学基金(10701059)资助项目 （10701059）
