平衡问题和不动点问题的并行外梯度-粘性方法
Parallel extragradient - viscosity methods for equilibrium problems and fixed point problems
摘要：
本文提出了两种并行的外梯度-粘性方法，分别用于求平衡问题组和多个不动点问题组的公共解集中的一个特殊元素。这个特殊点是变分不等式问题在公共解集上的唯一解。本文的主要思想是将超梯度法、Mann迭代法、混合最速下降法与并行分裂技术相结合，设计出性能优于现有方法的算法。在平衡双函数广泛使用的假设下，建立了强收敛定理。
英文摘要：
In this paper, we propose two parallel extragradient - viscosity methods for finding a particular element in the common solution set of a system of equilibrium problems and finitely many fixed point problems. This particular point is the unique solution of a variational inequality problem on the common solution set. The main idea of the paper is to combine three methods including the extragradient method, the Mann iteration method, the hybrid steepest-descent method with the parallel splitting-up technique to design the algorithms which improve the performance over some existing methods. The strongly convergent theorems are established under the widely used assumptions for equilibrium bifunctions.
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