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

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 395-407.

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

蔡钢()

^{重庆师范大学数学科学学院重庆 401331}

收稿日期:2018-11-20 出版日期:2020-04-26 发布日期:2020-05-21
作者简介:蔡钢, E-mail:caigang-aaa@163.com
基金资助:
国家自然科学基金(11971082);国家自然科学基金(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)

Viscosity Implicit Algorithms for a Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces

Gang Cai()

^{School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331}

Received:2018-11-20 Online:2020-04-26 Published:2020-05-21
Supported by:
the NSFC(11971082);the NSFC(11771063);the NSF of Chongqing(cstc2017jcyjAX0006);the Science and Technology Project of Chongqing Education Committee(KJZD-K201900504);the University Young Core Teacher Foundation of Chongqing(020603011714);the Talent Project of Chongqing Normal University(02030307-00024)

摘要/Abstract

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.

关键词: Hilbert空间, 非扩张映射, 变分不等式, 强收敛

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.

Key words: Hilbert spaces, Nonexpansive mapping, Variational inequality, Strong convergence

中图分类号:

O177

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, 2020, 40(2): 395-407.

Gang Cai. Viscosity Implicit Algorithms for a Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces[J]. Acta mathematica scientia,Series A, 2020, 40(2): 395-407.

参考文献 17

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