关于伪单调变分不等式与不动点问题的新投影算法

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 904-919.

关于伪单调变分不等式与不动点问题的新投影算法

杨静(),龙宪军*()

^{重庆工商大学数学与统计学院重庆 400067}

收稿日期:2021-08-12 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 龙宪军 E-mail:jyang1230@163.com;xianjunlong@ctbu.edu.cn
作者简介:杨静, E-mail: jyang1230@163.com
基金资助:
国家自然科学基金(11471059);重庆市自然科学基金(cstc2021jcyj-msxmX0721);重庆市教育委员会科学技术研究重点项目(KJZD-K201900801)

A New Projection Algorithm for Solving Pseudo-Monotone Variational Inequality and Fixed Point Problems

Jing Yang(),Xianjun Long*()

^{College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067}

Received:2021-08-12 Online:2022-06-26 Published:2022-05-09
Contact: Xianjun Long E-mail:jyang1230@163.com;xianjunlong@ctbu.edu.cn
Supported by:
NSFC(11471059);the NSF of Chongqing(cstc2021jcyj-msxmX0721);the Education Committee Project Research Foundation of Chongqing(KJZD-K201900801)

摘要/Abstract

摘要：

该文在Hilbert空间中给出了一个新投影算法，找到了伪单调变分不等式问题的解集与半压缩映射的不动点集的公共元.在映射是伪单调和一致连续的条件下，证明了强收敛定理.数值实验结果表明了新算法的有效性和优越性.

关键词: 变分不等式, 不动点, 投影算法, 一致连续, 伪单调

Abstract:

In this paper, we propose a new projection algorithm for finding a common element of psedomonotone variational inequality problems and fixed point set of demicontractive mappings in Hilbert spaces. We prove that this new algorithm converges strongly to the common element for a psedomonotone and uniformly continuous mapping. Finally, we provide some numerical experiments to illustrate the efficiency and advantages of the new projection algorithm.

Key words: Variational inequality, Fixed point, Projection algorithm, Uniformly continuous, Pseudomonotone

中图分类号:

O224

杨静,龙宪军. 关于伪单调变分不等式与不动点问题的新投影算法[J]. 数学物理学报, 2022, 42(3): 904-919.

Jing Yang,Xianjun Long. A New Projection Algorithm for Solving Pseudo-Monotone Variational Inequality and Fixed Point Problems[J]. Acta mathematica scientia,Series A, 2022, 42(3): 904-919.

参考文献

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