摘要
基于Peng给出的变分不等式的势函数,提出修正梯度路径与仿射变换内点法解线性不等式约束的变分不等式问题.借助于对称矩阵的特征分解与仿射变换映射,可以构建修正梯度路径.进一步使用路径搜索并结合内点回代线搜索技巧,近似地求解信赖域子问题;最后在合理的假设条件下,证明了算法具有整体收敛性.
Based on the merit function proposed by Peng, we present the modified gradient path and affine scaling interior method for variational inequality problems with linear inequality constraints. We employ eigensystem decomposition and affine scaling mapping to form the modified gradient path. By searching the step along the path and using interior backtracking line search technique, the trust region subproblem can be approximately solved. Under some reasonable conditions, the global convergence is established .
出处
《上海师范大学学报（自然科学版）》
2008年第4期331-339,共9页
Journal of Shanghai Normal University(Natural Sciences)
基金
The authors gratefully acknowledge the partial supports of the Science Foundation Grant(05DZ11,06A110)of Shanghai Education Committee.
关键词
变分不等式问题
仿射
内点
回代
非单调技术
修正梯度路径
收敛
variational inequality problem
atone scaling
interior point
backtracking
nonmonotonic technique
modified gradient path
convergence
