| 广义集值强非线性混合似变分不等式解的存在性与算法 |
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| 引用本文： | 曾六川. 广义集值强非线性混合似变分不等式解的存在性与算法[J]. 工程数学学报, 2006, 23(2): 324-332 |
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| 作者姓名： | 曾六川 |
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| 作者单位： | 上海师范大学数学系,上海,200234 |
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| 基金项目： | The Shanghai Leading Academic Discipline Project N. T0401; the Dawn Program Foundation in Shanghai. The author expresses his heartfelt gratitude to the referee for his valuable and helpful suggestions. |
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| 摘 要： | 本文延拓辅助原理的技巧,来研究一类广义集值强非线性混合似变分不等式。首先,利用Ky Fan引理,证明了这类混合似变分不等式的辅助问题解的存存性。其次,利用该存在性结果,给出了解这类混合似变分不等式的迭代算法。最后。既证明了这类混合似变分不等式解的存在性,又证明了由算法生成的迭代序列的收敛性。
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| 关 键 词： | 混合似变分不等式 辅助原理的技巧 迭代算法 集值映象 存在性 收敛性 |
| 文章编号： | 1005-3085(2006)02-0324-09 |
| 收稿时间： | 2003-09-15 |
| 修稿时间： | 2003-09-15 |
Existence and Algorithm of Solutions for Generalized Set-valued Strongly Nonlinear Mixed Variational-like Inequalities |
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| ZENG Liu-chuan. Existence and Algorithm of Solutions for Generalized Set-valued Strongly Nonlinear Mixed Variational-like Inequalities[J]. Chinese Journal of Engineering Mathematics, 2006, 23(2): 324-332 |
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| Authors: | ZENG Liu-chuan |
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| Affiliation: | Department of Mathematics, Shanghai Normal University, Shanghai 200234 |
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| Abstract: | The auxiliary principle technique is extended to investigate a class of generalized set-valued strongly nonlinear variational-like inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of mixed variational-like inequalities is shown by virtue of Ky Fan's lemma. Secondly, the iterative algorithm for solving this class of mixed variational like inequalities is given by using this existence result. Finally, not only the existence of solutions of this class of mixed variational-like inequalities is shown, but also the convergence of iterative sequences generated by the algorithm is proven. |
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| Keywords: | mixed variational-like inequality auxiliary principle technique iterative algorithm |
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