Hilbert空间中广义变分不等式的投影算法  

A Projected Method for Solving Generalized Variational Inequalities in Hilbert Spaces

作　　者：李涛[1] 夏福全[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2011年第5期610-614,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10671135;70831005);四川省教育厅自然科学重点基金(09ZA091)资助项目

摘　　要：在Hilbert空间中研究了广义变分不等式的投影算法.在算法的每一步,首先在集值映象T中选取适当的点,然后将它投影到变分不等式的可行集上,获得下一步的迭代点.在集值映象为伪单调*的条件下,证明了迭代序列弱收敛于广义变分不等式的解.In this paper,we consider the projection method for solving generalized variational inequalities in Hilbert spaces.We investigate a general iterative algorithm.In each step,we select a point in the set-valued mapping T followed by a projection onto the feasible set of the generalized variational inequality.Under the assumption that the set-valued mapping is pseudomonotone＊,we prove that the iterative sequences is weakly convergent and the weak limit point is the solution of generalized variational inequalities.

关 键 词：投影算法 弱收敛 伪单调＊映象 

分 类 号：O176.3[理学—数学] O178[理学—基础数学]