Tian Ming, Jiang Bing-Nan
College of Science, Civil Aviation University of China, Tianjin, 300300 China.
J Inequal Appl. 2017;2017(1):123. doi: 10.1186/s13660-017-1397-9. Epub 2017 May 25.
In this paper, we consider the algorithm proposed in recent years by Censor, Gibali and Reich, which solves split variational inequality problem, and Korpelevich's extragradient method, which solves variational inequality problems. As our main result, we propose an iterative method for finding an element to solve a class of split variational inequality problems under weaker conditions and get a weak convergence theorem. As applications, we obtain some new weak convergence theorems by using our weak convergence result to solve related problems in nonlinear analysis and optimization.
在本文中，我们考虑了近年来由森索尔、吉巴利和赖希提出的用于解决分裂变分不等式问题的算法，以及用于解决变分不等式问题的科尔佩列维奇外梯度法。作为我们的主要成果，我们提出了一种迭代方法，用于在较弱条件下找到一个元素来解决一类分裂变分不等式问题，并得到了一个弱收敛定理。作为应用，我们通过利用我们的弱收敛结果来解决非线性分析和优化中的相关问题，获得了一些新的弱收敛定理。
