非单调变分不等式黄金分割算法研究

杨军

doi:10.21656/1000-0887.410359

非单调变分不等式黄金分割算法研究

doi: 10.21656/1000-0887.410359

杨军^,

咸阳师范学院数学与信息科学学院，陕西咸阳 712000

详细信息

作者简介:
杨军(1980—)，男，博士(E-mail: xysyyangjun@163.com).

通讯作者:
杨军(1980—)，男，博士(E-mail: xysyyangjun@163.com).

中图分类号: O221.2
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- 被引次数: 0
出版历程
- 收稿日期: 2020-11-24
- 修回日期: 2021-04-30

A Golden Ratio Algorithm for Solving Nonmonotone Variational Inequalities

YANG Jun^,

College of Mathematics and Information Science, Xianyang Normal University,Xianyang, Shaanxi 712000, P.R.China

摘要

摘要: 该文考虑变分不等式的梯度投影算法，给出了一种非单调变分不等式的黄金分割算法,所给出的算法特点结合了惯性加速方法,无需知道映射的Lipschitz常数,且步长是非单调递减的.在一定的条件下,算法的收敛性被证明.最后给出数值实验结果.
- 变分不等式 /
- 投影 /
- 非单调映射
Abstract: A gradient projection method was considered for solving variational inequalities, and a golden ratio gradient algorithm for solving nonmonotonic mapping was given. The characteristics of the algorithm combine those of the inertial acceleration method, without the knowledge of the mapping’s Lipschitz constant but with a nonmonotonically decreasing step size. Under suitable assumptions, the convergence of the algorithm was proved. Finally, numerical experiments were given.
- variational inequality /
- projection /
- nonmonotone mapping

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参考文献(17)

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