求解伪单调型变分不等式的一种投影算法  

A Projection Algorithm for Solving Pseudomonotone Variational Inequalities

作　　者：陈园 何诣然 CHEN Yuan;HE Yiran(School of Mathematical Science,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2020年第3期297-303,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省科技厅应用基础项目(2018JY0201)。

摘　　要：在投影收缩算法的基础上,通过构造一种超平面,给出求解伪单调型变分不等式的一种投影算法,并证明该算法在变分不等式解集非空且F为伪单调连续映射的条件下是全局收敛的.在该算法生成的序列满足某种误差界条件下,得到算法的收敛率.最后,用数值实验对比所提算法与已知4种算法的收敛效果.In this paper,based on projection and contraction method,we introduce a projection algorithm for solving pseudomonotone variational inequalities. If the solution of the varational inequality does exist and F is a continuous and pseudomonotone mapping,the sequence produced by our method globally converges to a solution. If a certain error bound holds,the convergence rate of the iterative sequence is established. Finally,numerical experiments are reported.

关 键 词：变分不等式 投影算法 超平面 

分 类 号：O22[理学—运筹学与控制论] O177.92[理学—数学]