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一种新的截断混合谱共轭梯度法

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共轭梯度法具有储存小、计算快的优点,对于解决大规模问题具有比较明显的优点。本文基于PRP类的参数类型,修正了 HS参数,同时为了保证算法既有较好的数值效果,又具有FR类好的收敛性质,对此设计了一种截断混合共轭参数,在此基础上设计了新的谱共轭参数。并用强Wolfe线搜索条件证明了该算法具有全局收敛性。最后通过对CUTEr测试集里面的问题进行数值实验,结果发现该算法相比其他三类方法,具有较好的数值效果。
A new truncated mixed spectrum conjugate gradient method
The conjugate gradient method has the advantages of small storage and fast computation,and has obvious ad-vantages for solving large-scale problems.This article modifies the HS parameter based on the parameter types of the PRP class,while ensuring that the algorithm not only has good numerical performance,but also hopes to have good convergence properties of FR.A truncated mixed conjugation parameter was designed for this,and a new spectral conjugation parameter was designed based on this.This article proves that the algorithm has global convergence using strong Wolfe line search condi-tions.Finally,through numerical experiments on the problems in the CUTEr test set,it was found that the algorithm has bet-ter numerical performance compared to the other three types of methods.

unconstrained optimizationtruncated mixed spectrum conjugate gradient methodglobal convergence

古恒洋、胡鹏

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重庆师范大学数学科学学院,重庆 401331

无约束优化 截断混合谱共轭梯度法 全局收敛性

国家自然科学基金面上项目重庆师范大学研究生科研创新项目

12371258YKC23001

2024

内江师范学院学报
内江师范学院

内江师范学院学报

影响因子:0.299
ISSN:1671-1785
年,卷(期):2024.39(8)