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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 ›› 2015, Vol. 32 ›› Issue (3): 381-390.doi: 10.3969/j.issn.1005-3085.2015.03.007

• • 上一篇    下一篇

一类修正Zhang H. C.非单调共轭梯度算法

陈颖梅,   孙清滢   

  1. 中国石油大学(华东)理学院，青岛 266580
  • 收稿日期:2013-10-25 接受日期:2014-10-09 出版日期:2015-06-15 发布日期:2015-08-15
  • 基金资助:
    国家自然科学基金 (61201455; 61170319).

A Class of Modified Conjugate Gradient Methods with Zhang H. C. Non-monotone Rule

CHEN Ying-mei,   SUN Qing-ying   

  1. College of Science, China University of Petroleum (Huadong), Qingdao 266580
  • Received:2013-10-25 Accepted:2014-10-09 Online:2015-06-15 Published:2015-08-15
  • Supported by:
    The National Natural Science Foundation of China (61201455; 61170319).

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摘要： 为有效求解大规模无约束优化问题，本文基于RMFI共轭梯度法，结合Zhang H.C.非单调线搜索步长规则，提出了一类新的共轭梯度算法．在适当的条件下，证明了新算法的全局收敛性．数值算例表明，新算法比Zhang H.C.非单调规则下的标准RMFI方法收敛速度更快，更有效．同时，本文进一步研究了Zhang H.C.非单调线搜索步长规则的一个基于强迫函数的拓展模型，并从理论上证明了基于此拓展模型的新算法的全局收敛性．

关键词: 非单调线搜索, 共轭梯度算法, 共轭梯度参数, 全局收敛

Abstract:

Based on the RMFI conjugate gradient method and the Zhang H.C. non-monotone line search method, a new kind of conjugate gradient methods for solving large scale unconstrained optimization problems is presented. Under mild conditions, the proposed method with the Zhang H.C. line search method converges globally. Numerical results show that the new method is more efficient when compared with the RMFI method with the Zhang H.C. rule. In addition, we extend the Zhang H.C. non-monotone line search method by utilizing the forcing function, and theoretically, we have proved the new conjugate gradient methods' global convergence with the extended model. 

Key words: non-monotone linear search, conjugate gradient method, conjugate gradient coefficient, global convergence

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