伪单调变分不等式解集与拟非扩张映射不动点集公共元的强收敛定理

Strong Convergence Theorem for Pseudomonotonic Variational Inequality Solution Sets and Quasi-non-expansionary Mapping Fixed Point Sets Common Elements

在Hilbert空间中提出一种新的关于求解伪单调变分不等式问题的Tseng外梯度算法。在适当条件下,证明由此算法生成的迭代序列强收敛于伪单调变分不等式问题的解集与拟非扩张映射不动点集的公共元,并用数值实验说明所提算法的有效性。

A new Tseng outer gradient algorithm for solving pseudomonotonic variational inequality problems is proposed in Hilbert space.Under appropriate conditions,it is proved that the iterative sequence generated by the algorithm strongly converges to the common element of the solution set of pseudomonotonic variational inequality problem and the set of fixed points of the quasi-non-expansion map,and numerical experiments are given to illustrate the effectiveness of the proposed algorithm.