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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (2): 388-396.doi: 10.3969/j.issn.1005-3085.2025.02.013

• • 上一篇    

一种充分下降的新谱共轭梯度法

王森森1,   韩  信2,3,   苏  醒4   

  1. 1. 新疆和田学院数理学院，和田 848000
    2. 四川文理学院数学学院，达州 635000
    3. 西南大学电子信息工程学院，重庆 400715
    4. 北京工业大学计算机学院，北京 100124
  • 收稿日期:2023-09-03 接受日期:2024-09-24 出版日期:2025-04-15 发布日期:2025-06-15
  • 通讯作者: 韩信 E-mail: hanmath@163.com
  • 基金资助:
    国家自然科学基金(62276011)；政务数据安全达州市重点实验室一般项目(ZSAQ202311)；和田地区科技局项目(20220210)；“多维数据感知与智能信息处理”达州市重点实验室一般项目(DWSJ2405).

A New Spectral Conjugate Gradient Method with Sufficient Descent Property

WANG Sensen1,   HAN Xin2,3,   SU Xing4   

  1. 1. School of Mathematics and Physics, Xinjiang Hetian College, Hetian 848000
    2. School of Mathematics, Sichuan University of Arts and Science, Dazhou 635000
    3. College of Electronics and Information Engineering, Southwest University, Chongqing 400715
    4. School of Computer Science, Beijing University of Technology, Beijing 100124
  • Received:2023-09-03 Accepted:2024-09-24 Online:2025-04-15 Published:2025-06-15
  • Contact: X. Han. E-mail address: hanmath@163.com
  • Supported by:
    The National Natural Science Foundation of China (62276011); the Dazhou Key Laboratory of Government Data Security (ZSAQ202311); the Hetian Regional Science and Technology Bureau Project (20220210); the Open Research Fund of the Dazhou City Key Laboratory of Multidimensional Data Perception and Intelligent Information Processing (DWSJ2405).

摘要：

基于修正的FR型谱共轭梯度法，对共轭参数和谱系数进行改进，提出一种具有充分下降性的谱共轭梯度法，该算法在标准Wolfe线搜索准则下具有全局收敛性。最后通过数值实验，将新算法与其他文献提出的两种FR型谱共轭梯度法进行比较，数值结果表明新算法在数值计算上具有一定的优势。

关键词: 无约束优化, 谱共轭梯度法, 标准Wolfe线搜索, 充分下降, 全局收敛

Abstract:

Based on the modified FR type spectral conjugate gradient method, the conjugate parameters and spectral coefficients are improved, and hence a sufficiently descending spectral conjugate gradient method is proposed. The spectral conjugate gradient method's global convergence is established under the standard Wolfe line search criteria. Finally, numerical experiments are carried out to compare the proposed method with two FR spectral conjugate gradient methods proposed in other literatures. The numerical results indicate that the proposed method enjoys certain advantages in numerical calculation.

Key words: unconstrained optimization, spectral conjugate gradient method, standard Wolfe line search, sufficient descent, global convergence

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