一种 WYL 型谱共轭梯度法的全局收敛性

数学物理学报 ›› 2024, Vol. 44 ›› Issue (1): 173-184.

一种 WYL 型谱共轭梯度法的全局收敛性

蔡宇(),周光辉^*()

淮北师范大学数学科学学院安徽淮北 235000

收稿日期:2022-11-07 修回日期:2023-10-16 出版日期:2024-02-26 发布日期:2024-01-10
通讯作者: 周光辉, E-mail:163zgh@163.com
作者简介:蔡宇, E-mail:caiyumaths@163.com
基金资助:
安徽省高校自然科学研究项目(KJ2020ZD008)

Global Convergence of a WYL Type Spectral Conjugate Gradient Method

Cai Yu(),Zhou Guanghui()

School of Mathematical Sciences, Huaibei Normal University, Anhui Huaibei 235000

Received:2022-11-07 Revised:2023-10-16 Online:2024-02-26 Published:2024-01-10
Supported by:
NSF of Anhui Province(KJ2020ZD008)

摘要/Abstract

摘要：

为解决大规模无约束优化问题, 该文结合 WYL 共轭梯度法和谱共轭梯度法, 给出了一种 WYL 型谱共轭梯度法. 在不依赖于任何线搜索的条件下, 该方法产生的搜索方向均满足充分下降性, 且在强 Wolfe 线搜索下证明了该方法的全局收敛性. 与 WYL 共轭梯度法的收敛性相比, WYL 型谱共轭梯度法推广了线搜索中参数$\sigma$的取值范围. 最后, 相应的数值结果表明了该方法是有效的.

关键词: 无约束优化, 谱共轭梯度法, 强 Wolfe 线搜索, 全局收敛性

Abstract:

In order to solve large scale unconstrained optimization problems, this paper combines the WYL conjugate gradient method with the spectral conjugate gradient method to give a WYL type spectral conjugate gradient method. Without relying on any line search, the search directions generated by the method satisfy the sufficient descent condition. Compared with the convergence of the WYL conjugate gradient method, the spectral WYL conjugate gradient method extends the range of values of the parameter$\sigma$in the line search. Finally, the corresponding numerical results show that the method is effective.

Key words: Unconstrained optimization, Spectral conjugate gradient method, Strong Wolfe line search, Global convergence

中图分类号:

O221

蔡宇, 周光辉. 一种 WYL 型谱共轭梯度法的全局收敛性[J]. 数学物理学报, 2024, 44(1): 173-184.

Cai Yu, Zhou Guanghui. Global Convergence of a WYL Type Spectral Conjugate Gradient Method[J]. Acta mathematica scientia,Series A, 2024, 44(1): 173-184.

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