| Hilbert空间中关于变分不等式问题和不动点问题的粘性隐式中点算法 |
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| 引用本文： | 蔡钢.Hilbert空间中关于变分不等式问题和不动点问题的粘性隐式中点算法[J].数学物理学报(A辑),2020(2):395-407. |
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| 作者姓名： | 蔡钢 |
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| 作者单位： | 重庆师范大学数学科学学院 |
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| 基金项目： | 国家自然科学基金(11971082,11771063);重庆市自然科学基金(cstc2017jcyjAX0006);重庆市教委项目(KJZD-K201900504);重庆市高等学校青年骨干教师资助计划(020603011714);重庆师范大学青年拔尖人才计划(02030307-00024)。 |
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| 摘 要： | 该文在Hilbert空间中研究了关于两个逆强单调算子的一般变分不等式问题和非扩张映射的不动点问题的粘性隐式中点算法,用修改的超梯度方法,在对参数作适当的限制下,得到了强收敛定理,所得结果推广和提高了许多最新文献中的相应结果.
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| 关 键 词： | HILBERT空间 非扩张映射 变分不等式 强收敛 |
Viscosity Implicit Algorithms for a Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces |
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| Cai Gang.Viscosity Implicit Algorithms for a Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces[J].Acta Mathematica Scientia,2020(2):395-407. |
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| Authors: | Cai Gang |
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| Institution: | (School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331) |
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| Abstract: | In this paper,we study a viscosity implicit algorithm for finding a common element of the set of solutions of a new variational inequality problems for two inverse-strongly monotone operators and the set of fixed points of a nonexpansive mapping in Hilbert spaces.Using modified extragradient method,we obtain strong convergence theorems under some suitable assumptions imposed on the parameters.The results obtained in this paper extend and improve many recent ones. |
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| Keywords: | Hilbert spaces Nonexpansive mapping Variational inequality Strong convergence |
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