与渐进非扩张半群不动点问题有关的分裂变分包含问题及其对最优化问题的应用

数学物理学报 ›› 2018, Vol. 38 ›› Issue (2): 231-243.

与渐进非扩张半群不动点问题有关的分裂变分包含问题及其对最优化问题的应用

张石生¹, 刘振海², 温庆丰³, 唐金芳⁴

1. 中国医药大学通识教育中心台湾台中 40402;
2. 广西民族大学南宁 530006;
3. 高雄医药大学基础科学中心, 非线性分析及最优化研究中心台湾高雄 80702;
4. 宜宾学院四川宜宾 644007

收稿日期:2016-07-21 修回日期:2017-04-29 出版日期:2018-04-26 发布日期:2018-04-26
通讯作者: 张石生 E-mail:changss2013@163.com
作者简介:刘振海,E-mail:zhhliu100@gmail.com;温庆丰,E-mail:cfwen@kmu.edu.tw
基金资助:
国家自然科学基金（11671101）、广西杰出专家特别基金、台中中国医药大学及高雄医药大学非线性分析及最优化研究中心自然科学基金和四川省科技厅科学研究基金（2015JY0165）

Split Variational Inclusion Problem Involving Fixed Point for an Asymptotically Nonexpansive Semigroup with Application to Optimization Problem

Chang Shih-sen¹, Liu Zhenhai², Wen Ching-Feng³, Tang Jinfang⁴

1. Center for General Education, China Medical University, Taiwan Taichung 40402;
2. Guangxi University for Nationalities, Nanning, Guangxi 53006;
3. Center for Fundamental Science, Kaohsiung Medical University, Taiwan Kaohsiung 80708;
4. Yibin University, Sichuan Yibin 644007

Received:2016-07-21 Revised:2017-04-29 Online:2018-04-26 Published:2018-04-26
Supported by:
Supported by the NSFC (11671101), the Guangxi Special Fund for Qutstanding Experts, the Natural Science Foundation of Taichung China Medical University and Nonlinear Analysis and Optimization Research Center of Kaohsiung Medical University, and the Scientific Research Fund of Sichuan Provincial Department of Science and Technology (2015JY0165)

摘要/Abstract

摘要： 该文的目的是利用收缩投影方法，引入一类迭代程序，并证明该迭代程序强收敛于Hilbert空间中分裂变分包含问题和渐进非扩张半群的不动点问题的一公解.作为应用，在文中还把所得结果应用于研究分裂最优化问题及分裂变分不等式问题.

关键词: 分裂变分包含问题, 渐进非扩张半群, 不动点问题, 非扩张半群

Abstract: The purpose of this paper is by using the shrinking projection method to introduce and study an iterative process to approximate a common solution of split variational inclusion problem and fixed point problem for an asymptotically nonexpansive semigroup in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and fixed point problem for an asymptotically nonexpansive semigroup. As applications, we shall utilize the results to study the split optimization problem and the split variational inequality.

Key words: Split variational inclusion problem, Asymptotically nonexpansive semigroup, Fixed point problem, Nonexpansive semigroup

中图分类号:

O177.91

张石生, 刘振海, 温庆丰, 唐金芳. 与渐进非扩张半群不动点问题有关的分裂变分包含问题及其对最优化问题的应用[J]. 数学物理学报, 2018, 38(2): 231-243.

Chang Shih-sen, Liu Zhenhai, Wen Ching-Feng, Tang Jinfang. Split Variational Inclusion Problem Involving Fixed Point for an Asymptotically Nonexpansive Semigroup with Application to Optimization Problem[J]. Acta mathematica scientia,Series A, 2018, 38(2): 231-243.

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