一种改进的推广近中心点算法

A modified generalized proximal point algorithm for variational inequalities

考虑变分不等式问题,基于D.Han(2003)提出的推广近中心点算法,通过改进算法的投影区域,提出了求解变分不等式问题的一种新的推广近中心点算法.该算法具有如下特点:算法产生的迭代点列关于初始点具有扩张性质;如果变分不等式问题有解,则算法产生的迭代点列的极限点就是初始点到问题解集上的投影;在适当的假设条件下,算法具有全局收敛性.最后,给出了该算法的初步数值试验结果.

The variational inequality problem is considered in this paper.Based on Han＇s work（2003）,proposed an improved generalized proximal point algorithm for solving variational inequalities by modifying the original projection region with the following features：the sequence generated by the algorithm has an expansion property with repect to the initial point;if the solution set of the variational inequality problem is nonempty,then the limit point of the sequence generated by the improved algorithm is just the projection of the initial point onto the solution set.Under suitable assumptions,the algorithm has the global convergence.The preliminary numerical test results are also reported here.