陈欢欢,李耿华

• 1:重庆工商大学数学与统计学院

摘要(Abstract)：

在实希尔伯特中，基于已有的求解非单调变分不等式问题的算法，提出了一类改进的惯性投影收缩算法.该算法通过引入惯性项的方式提出了一种带有Armijo线搜索的惯性次梯度算法，使更新过程中既利用了当前梯度信息，又考虑了先前的迭代方向，从而在加速收敛的同时避免了传统投影算法中可能出现的震荡问题，分析了该算法的收敛性并给出了理论证明，表明在一定条件下算法具有全局收敛性.并结合数值实验验证了改进的算法的有效性.

关键词(KeyWords)： 变分不等式;强收敛;Lipschitz连续;非单调

Abstract:

Keywords:

基金项目(Foundation): 青年科学基金项目(12001070);; 重庆市自然科学基金面上项目(cstc2020jcyj-msxmX0231);; 重庆市教委自然科学基金项目(KJQH202400833);; 重庆市研究生科研创新项目(yjscxx2024-284-243)

作者(Author): 陈欢欢,李耿华

DOI: 10.16393/j.cnki.37-1436/z.2025.02.014

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