[1]葛志利,谭志聪,徐莹莹,等.一类带线性约束的变分不等式的预测校正方法的收敛率分析[J].南京师大学报(自然科学版),2024,(03):1-7.[doi:10.3969/j.issn.1001-4616.2024.03.001]
　Ge Zhili,Tan Zhicong,Xu Yingying,et al.Convergence Rate Analysis of Prediction Correction Methods for a Class of Variational Inequalities with Linear Constraints[J].Journal of Nanjing Normal University(Natural Science Edition),2024,(03):1-7.[doi:10.3969/j.issn.1001-4616.2024.03.001]
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一类带线性约束的变分不等式的预测校正方法的收敛率分析()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
期数:
2024年03期
页码:
1-7
栏目:
数学
出版日期:
2024-09-15

文章信息/Info

Title:
Convergence Rate Analysis of Prediction Correction Methods for a Class of Variational Inequalities with Linear Constraints
文章编号:
1001-4616(2024)03-0001-07
作者:
葛志利1; 谭志聪1; 徐莹莹2; 张 欣3
(1.南京特殊教育师范学院数学与信息科学学院,江苏 南京 210038)
(2.东南大学信息科学与工程学院,江苏 南京 211189)
(3.宿迁学院文理学院,江苏 宿迁 223800)
Author(s):
Ge Zhili1; Tan Zhicong1; Xu Yingying2; Zhang Xin3
(1.School of Mathematics and Information Science,Nanjing Normal University of Special Education,Nanjing 210048,China)
(2.School of Information Science and Engineering,Southeast University,Nanjing 211189,China)
(3.School of Arts and Science,Suqian University,Suqian 223800,China)
关键词:
线性约束; 变分不等式; 全局线性收敛性; 预测校正方法
Keywords:
linear constraints; variational inequalities; global linear convergence; prediction correction method
分类号:
O221.4
DOI:
10.3969/j.issn.1001-4616.2024.03.001
文献标志码:
A
摘要:
考虑一类带线性约束的变分不等式问题:寻找x*∈Ω满足F(x*)T(x-x*)≥0,x∈Ω,其中Ω={x∈Rn|Ax≤b,x∈K},A∈Rm×n,b∈Rm,K是Rn上的一个简单的非空闭凸子集,F是Rn到Rn的连续未知算子且满足强单调. 对此类问题,本文研究了一种新的预测校正方法. 根据已有的收敛性结果,利用误差界条件进一步分析了该方法的线性收敛性. 最后,通过交通均衡问题中两个带线性约束例子的数值结果展示了算法的有效性.
Abstract:
This paper considers a class of variational inequalities with linear constraints:finding x*∈Ω,such that F(x*)T(x-x*)≥0,x∈Ω,where Ω={x∈Rn|Ax≤b,x∈K},A∈Rm×n,b∈Rm,K is a simple nonempty closed convex subset of Rn,F is a continuous unknown mapping from Rn to Rn,and satisfies the strong monotonicity. We study a new prediction correction method for this class of problems. Based on the previous convergence results,we further analyze the linear convergence by using the error bound condition. Finally,two numerical results in traffic equilibrium problems with linear constraints demonstrate the effectiveness of the algorithm.

参考文献/References:

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相似文献/References:

[1]孙黎明.一种求解线性规划的投影动态方法（英文）[J].南京师大学报(自然科学版),2015,38(04):8.
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备注/Memo

备注/Memo:
收稿日期:2023-06-03.
基金项目:国家自然科学基金项目(120081)、江苏省青蓝工程项目、宿迁市科技计划资助项目(M202206)、宿迁学院高级别纵向科研培育项目.
通讯作者:徐莹莹,博士研究生,研究方向:移动网络通信优化. E-mail:vivi_xuyingying@163.com
更新日期/Last Update: 2024-09-15