| 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 |
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| 引用本文： | 王云娟,朱德通,. 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[J]. 上海师范大学学报(自然科学版), 2008, 37(4): 331-339 |
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| 作者姓名： | 王云娟 朱德通 |
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| 作者单位： | 上海师范大学,数理信息学院,上海,200234;上海师范大学,商学院,上海,200234 |
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| 基金项目： | the Science Foundation Grant，上海市教委资助项目 |
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| 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．
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| 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 收剑 |
The modified gradient path and affine scaling interior method for variational inequality problems with linear inequality constraints |
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| WANG Yun-juan,ZHU De-tong. The modified gradient path and affine scaling interior method for variational inequality problems with linear inequality constraints[J]. Journal of Shanghai Normal University(Natural Sciences), 2008, 37(4): 331-339 |
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| Authors: | WANG Yun-juan ZHU De-tong |
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| Affiliation: | WANG Yun-juan, ZHU De-tong ( 1. College of Mathematics and Sciences, Shanghai Normal University, Shanghai 200234, China 2. College of Business, Shanghai Normal University, Shanghai 200234, China) |
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| Abstract: | 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 . |
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| Keywords: | variational inequality problem affine scaling interior point backtracking nonmonotonic technique modified gradient path convergence |
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