求解伪单调型变分不等式的一种投影算法

A Projection Algorithm for Solving Pseudomonotone Variational Inequalities

在投影收缩算法的基础上,通过构造一种超平面,给出求解伪单调型变分不等式的一种投影算法,并证明该算法在变分不等式解集非空且F为伪单调连续映射的条件下是全局收敛的.在该算法生成的序列满足某种误差界条件下,得到算法的收敛率.最后,用数值实验对比所提算法与已知4种算法的收敛效果.

In this paper,based on projection and contraction method,we introduce a projection algorithm for solving pseudomonotone variational inequalities. If the solution of the varational inequality does exist and F is a continuous and pseudomonotone mapping,the sequence produced by our method globally converges to a solution. If a certain error bound holds,the convergence rate of the iterative sequence is established. Finally,numerical experiments are reported.