Hilbert 空间中变分不等式问题的自适应粘性算法

数学物理学报 ›› 2023, Vol. 43 ›› Issue (2): 581-592.

Hilbert 空间中变分不等式问题的自适应粘性算法

夏平静,蔡钢()

重庆师范大学数学科学学院重庆401331

收稿日期:2022-05-12 修回日期:2022-10-17 出版日期:2023-04-26 发布日期:2023-04-17
通讯作者: 蔡钢，E-mail：caigang-aaaa@163.com
基金资助:
国家自然科学基金(12171062);重庆市自然科学基金(CSTB2022NSCQ-JQX0004);重庆市教委重点项目(KJZD-K201900504)

Self Adaptive Viscosity Algorithm for Solving Variational Inequality Problem in Hilbert Spaces

Xia Pingjing,Cai Gang()

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331

Received:2022-05-12 Revised:2022-10-17 Online:2023-04-26 Published:2023-04-17
Supported by:
NSFC(12171062);Natural Science Foundation of Chongqing(CSTB2022NSCQ-JQX0004);Sciene and Technology Project of Chongqing Education Committee(KJZD-K201900504)

摘要/Abstract

摘要：

该文提出了一个新的自适应次超梯度粘性算法来求解 Hilbert 空间中的伪单调变分不等式问题. 应用新步长准则, 在不需要知道利普希茨常数的条件下得到了强收敛定理. 通过一些数值例子说明了所提算法的有效性.

关键词: 变分不等式, 伪单调映射, 自适应步长, 强收敛

Abstract:

In this paper, we propose a new self adaptive subgradient extragradient viscosity algorithm for solving pseudomonotone variational inequality problems in Hilbert space. Using the new stepsize rule, the strong convergence theorem is obtained without any information about the Lipschitz constant. The effectiveness of the suggested algorithm is illustrated through some numerical examples.

Key words: Variational inequality, Pseudomonotone mapping, Self adaptive stepsize, Strong convergence

中图分类号:

O177

夏平静, 蔡钢. Hilbert 空间中变分不等式问题的自适应粘性算法[J]. 数学物理学报, 2023, 43(2): 581-592.

Xia Pingjing, Cai Gang. Self Adaptive Viscosity Algorithm for Solving Variational Inequality Problem in Hilbert Spaces[J]. Acta mathematica scientia,Series A, 2023, 43(2): 581-592.

图/表 3

图1

例 4.1 中当 $\epsilon_n=10^{-4}$ 时所有算法的数值行为"

图1

图2

例 4.1 中当 $\epsilon_n=10^{-6}$ 时所有算法的数值行为"

图2

表1

参考文献 24

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