Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities
Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities
复制标题
一般变分不等式系统的松弛超梯度方法的强收敛定理
DOI：
10.1007/s00186-007-0207-4
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发表时间：
2008-06-01
影响因子：
1.2
通讯作者：
Yao, Jen-Chih
中科院分区：
文献类型：
--
作者：
Ceng, Lu-Chuan;Wang, Chang-yu;Yao, Jen-Chih
本文在真实的Hilbert空间中引入并研究了求解一般逆强单调变分不等式组的松弛外梯度方法.首先证明了该变分不等式组等价于非扩张映象的不动点问题。其次，利用非扩张映象的n-闭性原理，证明了在相当温和的条件下，由松弛外梯度法定义的迭代序列强收敛于该变分不等式组的解.此外，利用这一结果，我们提供了一些应用所考虑的问题，而不仅仅是给一个纯粹的扩展现有的数学问题。
In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point problem of nonexpansive mapping. Second, by using the demi-closedness principle for nonexpansive mappings, we prove that under quite mild conditions the iterative sequence defined by the relaxed extragradient method converges strongly to a solution of this system of variational inequalities. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems.