解非单调变分不等式投影算法的扰动分析

A Perturbation Analysis of Projection Method for Solving Variational Inequalities without Monotonicity

2015年叶与何提出了求解非单调变分不等式的二次投影算法,该算法的第k+1个迭代点由第k个迭代点向可行集与前k个半空间的交的投影来得到。从而随着k的增加,投影的计算也越来越复杂。本文对该算法做了扰动分析,证明了新迭代点在一定的误差影响下仍然能全局收敛到变分不等式的解。

In 2015,Ye and He proposed a double projection method for solving variational inequalities without monotonicity,by which the k+1th iteration point is obtained by projecting the kth iteration point onto the intersection of the feasible set and all of k half-spaces before.With the increasing of k,the calculation of projection becomes more and more complex.In this paper,the perturbation analysis of the method is presented.Under some assumptions about the error vector,the global convergence of the new iteration point to the solution of the variational inequality is proved.