广义混合变分不等式问题的投影算法  

The Projection Algorithm for Solving Generalized Mixed Variational Inequalities

作　　者：杨博[1] 夏福全[1] YANG Bo;XIA Fuquan(College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan)

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）》2018年第4期471-477,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：教育部科学技术重点项目(212147)

摘　　要：提出一种新的求解广义混合变分不等式的投影算法.在迭代的每一步,首先利用当前点xi,通过计算预解算子得到点z_i,其中的迭代步长满足某种Armijo线搜索.然后,利用zi构造出分离当前点xi及广义混合变分不等式解集的超平面,再将当前点向该超平面做投影得到下一步迭代点.在一定的条件下,给出该算法产生的无穷序列具有全局收敛性.同时,给出数值计算结果,表明这种算法的有效性.This paper presents a new projection algorithm for solving the generalized mixed variational inequalities. At each step of the iteration,the current point xiis first utilized,and the ziis obtained by calculating the resolvent operator,with the iteration step size satisfying with some kind of Armijo linesearch. Then,we use zito construct a superplane to separate the current point xiand solution set of generalized mixed variational inequalities. After that,the current point is projected into the superplane to get the next iteration point. Under certain conditions,the infinite sequence generated by the algorithm is globally convergent. At the same time,the numerical results show that the algorithm is effective.

关 键 词：广义混合变分不等式 投影算法 ARMIJO线搜索 超平面 

分 类 号：O176[理学—数学] O177[理学—基础数学]