| 广义集值强非线性混合似变分不等式解的迭代逼近 |
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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迭代逼近[J].数学学报,2005,48(5):879-888. |
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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： | 国家教育部高等学校优秀青年教师教学和科研奖励基金;上海市教委重点学科经费（部分）资助项目;上海市曙光计划基金资助项目 |
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| 摘 要： | 辅助原理的技巧被延拓来研究一类取非紧值的集值映象的广义强非线性混合似变分不等式.首先,证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性.其次,利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法.最后,不仅证明了这类广义强非线性混合似变分不等式解的存在性,而且证明了由算法生成的迭代序列的收敛性.
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| 关 键 词： | 迭代算法 集值映象 存在性 收敛性 |
| 文章编号： | 0583-1431（2005）05-0879-10 |
| 收稿时间： | 2003-09-29 |
| 修稿时间： | 2003-09-292004-07-15 |
Iterative Approximation of Solutions to Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities |
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| Ceng LiuChuan.Iterative Approximation of Solutions to Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities[J].Acta Mathematica Sinica,2005,48(5):879-888. |
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| Authors: | Ceng LiuChuan |
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| Institution: | Lu Chuan ZENG Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China |
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| Abstract: | The auxiliary principle technique is extended to study a class of generalized strongly nonlinear mixed variational-like inequalities for set-valued mappings without compact values. Firstly, the existence of solutions to the auxiliary problems for this class of generalized strongly nonlinear mixed variational-like inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized strongly nonlinear mixed variational-like inequalities is given by using this existence result. Finally, not only the existence of solutions of this class of generalized strongly nonlinear mixed variational-like inequalities is shown, but also the convergence of iterative sequences generated by the algorithm is proven. |
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| Keywords: | Iterative algorithm Set-valued mapping Existence Convergence |
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