| 无限维Hillbert空间中单调变分不等式解的近似迭代算法 |
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| 引用本文： | 邓汝良,丁协平.无限维Hillbert空间中单调变分不等式解的近似迭代算法[J].应用泛函分析学报,2004,6(3):245-249. |
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| 作者姓名： | 邓汝良 丁协平 |
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| 作者单位： | 1. 西南财经大学经济数学系,四川,成都,610074
2. 四川师范大学数学与软件科学院,四川,成都,610068 |
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| 基金项目： | 国家自然科学基金(19871059)，四川省教育厅基金([2000]25) |
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| 摘 要： | 在无穷维Hillbert空间中研究了一类单调型变分不等式，把求单调型变分不等式解的问题转化为求强单调变分不等式的解，建立了一种新的迭代算法，并证明了由算法生成的迭代序列强收敛于单调变分不等式的解，从而推广了所列文献中的许多重要结果．
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| 关 键 词： | 单调变分不等式 Hillbert空间 无限维 近似 迭代算法 强收敛 单调型 生成 迭代序列 |
| 文章编号： | 1009-1327(2004)03-0245-05 |
| 修稿时间： | 2002年12月10 |
Approximation Iterative Algorithms of Variational Inequalities with Monotone Mapping in Infinite Dimensional Hillbert Space |
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| DENG Ru-liang,DING Xie-ping.Approximation Iterative Algorithms of Variational Inequalities with Monotone Mapping in Infinite Dimensional Hillbert Space[J].Acta Analysis Functionalis Applicata,2004,6(3):245-249. |
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| Authors: | DENG Ru-liang DING Xie-ping |
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| Institution: | DENG Ru-liang~1,DING Xie-ping~21. Department of Economic Mathematics,Southwestern University of Finance and Economics,Chengdu Sichuan 610074,China2. College of Mathematics and Software Science,Sichuan Normal University,Chengdu Sichuan 610068,China |
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| Abstract: | A class of variational inequalities with monotone type is studied in infinite dimensional Hillbert space. By using the auxiliary variational inequality technique, the problem for solving variational inequalities with monotone mapping is transferred to solving variational inequalities with strongly monotone mapping. By constructing a new iterative algorithm, it is proved that iterative sequence generated by the new algorithm converge strongly to the solutions of variational inequalities with monotone mapping. The results generalizes many important results in literature. |
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| Keywords: | infinite dimensional Hillbert space monotone mapping differentiable strongly convex function |
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