| 一类包含松弛Lipschitz算子和松弛单调算子的广义变分不等式 |
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| 引用本文： | 雷飞燕,邢志栋.一类包含松弛Lipschitz算子和松弛单调算子的广义变分不等式[J].安徽大学学报(自然科学版),2008,32(2):15-17. |
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| 作者姓名： | 雷飞燕 邢志栋 |
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| 作者单位： | 1. 西安邮电学院,应用数理系,陕西,西安,710121
2. 西北大学,数学系,陕西,西安,710069 |
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| 基金项目： | 陕西省教育厅专向科研计划基金 |
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| 摘 要： | 主要利用松弛算子和单调算子性质,先给出松弛Lipschitz算子和松弛单调算子的特有性质,再将变分不等式与非线性方程的一些等价结论,推广到广义变分不等式上,然后利用这些结论,给出一类包含松弛算子和单调算子的广义变分不等式的迭代算法,并证明了算法的可行性.
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| 关 键 词： | 松弛算子 单调算子 广义变分不等式 连续算子 |
| 文章编号： | 1000-2162(2008)02-0015-03 |
| 修稿时间： | 2007年9月19日 |
One generalized variational inequality involving relaxed Lipschitz and relaxed monotone operators |
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| LEI Fei-yan,XING Zhi-dong.One generalized variational inequality involving relaxed Lipschitz and relaxed monotone operators[J].Journal of Anhui University(Natural Sciences),2008,32(2):15-17. |
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| Authors: | LEI Fei-yan XING Zhi-dong |
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| Abstract: | We used the nature of relaxed operator and monotone operator,first gave the unique nature of the relaxed Lipschitz operator and relaxed monotone operator.Then extended some equivalent conclusions of nonlinear equations and variational inequalities to the generalized variational inequalities,then used these conclusions,we gave an iterative algorithm for generalized variational ineqality involving relaxed Lipschitz and relaxed monotone operators.In the end,we proved the feasibility of the algorithm. |
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| Keywords: | relaxed operator monotone operator generalized variational inequality continuous operator |
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