伪单调变分不等式的次梯度外梯度投影算法

A Subgradient Exgradient Projection Method for Pseudomonotone Variational Inequalities

在有限维欧式空间中研究了Censor,Gibali和Reich意义下变分不等式的次梯度外梯度投影算法。在伪单调假设条件下,利用He和Liao所提出的线搜索条件,证明了由次梯度外梯度投影算法所产生的迭代序列强收敛到经典变分不等式的解。去掉了Censor,Gibali和Reich文章中关于变分不等式所涉及映像的Lipschitz连续性条件。

In this paper,we investigate a subgradient exgradient projection method for variational inequalities in the sense of Censor,Gibali and Reich in finite dimensional spaces. Under pseudomonotonicity assumptions,by using the linear search condition of He and Liao we prove the convergence of this subgradient exgradient projection method.Compared with the assumptions by Censor,Gibali and Reich,we remove the Lipschitz continuity condition.