对一个二步投影算法的改进以及它在变分不等式问题的应用  

Improvement of Two-Step Projection Method and Its Application to Variational Inequality

作　　者：徐述[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《云南民族大学学报（自然科学版）》2006年第4期279-280,284,共3页Journal of Yunnan Minzu University:Natural Sciences Edition

摘　　要：引入一个具有误差(参阅文献[1])的二阶投影算法,在Hilvert空间中利用它来讨论了一个非线性变分不等式组的解.设H是一个实Hilbert空间,K H非空闭凸锥,任意选择初始点x0,y0∈K.计算{xk},{yk},使得xk+1=(1-ak)xk+akPk(yk-ρT(yk))+ukρ>0yk=(1-bk)xk+bkPk(xk-ηT(xk))+vkη>0>0其中T:K→H:PK是H在K上的投影.0<ak,bk<1,结论推广了文献[2]的相应结果.First we introduce a two-step projection methods with errors. Then we discuss the solution of a system of variational inequalities in Hilbert space by using the two-step projection methods . Let H be a Hilbert space and K be a nonempty closed convex cone of H. For arbitrarily chosen initial points x0, Y0 ∈ K, we compute sequences of {x^k} and {y^k}I that make. x^k＋1=（1-a^k）x^k＋a^kPk（y^k-pT（y^k））＋u^k p〉0 y^k=（1-b^k）x^k＋b^kPk（x^k-ηT（x^k））＋v^k η〉0〉0 where T：K→H is a nonlinear mapping on K. Pk is the projection of H onto K, and 0 〈 a^k ,b^k 〈 1. The main theorem generalizes the result in the reference[ 2 ].

关 键 词：投影算法 非线性变分不等式 二步投影算法的收敛性 

分 类 号：O151.25[理学—数学]