一类拟单调变分不等式的惯性投影算法

数学物理学报 ›› 2023, Vol. 43 ›› Issue (2): 593-603.

一类拟单调变分不等式的惯性投影算法

杨蓝翔(),陈艺(),叶明露^*()

最优化理论与应用四川省高校重点实验室, 西华师范大学数学与信息学院四川南充 637009

收稿日期:2022-01-23 修回日期:2022-05-27 出版日期:2023-04-26 发布日期:2023-04-17
通讯作者: 叶明露，E-mail: yml2002cn@aliyun.com
作者简介:杨蓝翔，E-mail: 609497110@qq.com|陈艺，E-mail:cy1935393974@163.com
基金资助:
国家自然科学基金面上项目(11871059);西华师范大学培育项目(20A024);西华师范大学校级大学生创新创业训练计划项目(cxcy2022027)

Inertial Projection Algorithms for Quasimonotone Variational Inequalities

Yang Lanxiang(),Chen Yi(),Ye Minglu()

Sichuan Colleges and Universities Key Laboratory of Optimization Theory and Applications, School of Mathematics and Information, China West Normal University, Sichuan Nanchong 637009

Received:2022-01-23 Revised:2022-05-27 Online:2023-04-26 Published:2023-04-17
Supported by:
NSFC(11871059);Cultivation project of China West Normal University(20A024);Innovation and Entrepreneurship training Program for university students of China west normal university(cxcy2022027)

摘要/Abstract

摘要：

2020 年, Liu 和 Yang 在 Hilbert 空间中提出了一种求解拟单调变分不等式的投影算法. 该文介绍了一种新的惯性系数来加速 Liu 和 Yang 文中的算法, 并在相同的假设条件下得到了算法的全局弱收敛性. 数值实验表明适当选取参数后的惯性方法比 Liu 和 Yang 文中的算法有更少的迭代步数和计算机耗时.

关键词: 变分不等式, 投影算法, 拟单调, 惯性方法

Abstract:

In 2020, Liu and Yang proposed a projection algorithm (LY for short) for solving quasimonotone variational inequality in Hilbert Space. In this paper, by taking a new inertia coefficient, we present an inertial technique to accelerate LY. Under the same assumptions, the global weak convergence of the sequence generated by this algorithm is obtained. Numerical experiments show that the new algorithm can accelerate LY from the point view of iterate number steps and the point view of CPU time cost by taking suitable parameters.

Key words: Variational inequality, Projection algorithm, Quasimonotone, Inertial method

中图分类号:

O221

杨蓝翔, 陈艺, 叶明露. 一类拟单调变分不等式的惯性投影算法[J]. 数学物理学报, 2023, 43(2): 593-603.

Yang Lanxiang, Chen Yi, Ye Minglu. Inertial Projection Algorithms for Quasimonotone Variational Inequalities[J]. Acta mathematica scientia,Series A, 2023, 43(2): 593-603.

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