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一种求解非线性无约束优化问题的充分下降的共轭梯度法

Tsegay Giday Woldu1,*  张海斌1   张鑫1  张芳1   

  1. 1. 北京工业大学应用数理学院, 北京 100124
  • 收稿日期:2018-01-15 出版日期:2018-09-15 发布日期:2018-09-15
  • 通讯作者: Tsegay Giday Woldu E-mail: tsegay@emails.bjut.edu.cn
  • 基金资助:

    国家自然科学基金(Nos.  61179033, 11771003)

A sufficient descent conjugate gradient method for nonlinear unconstrained optimization problems

Tsegay Giday Woldu1,*   ZHANG Haibin1   ZHANG Xin1   ZHANG Fang1   

  1. 1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • Received:2018-01-15 Online:2018-09-15 Published:2018-09-15

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摘要：

共轭梯度法是一类具有广泛应用的求解大规模无约束优化问题的方法. 提出了一种新的非线性共轭梯度(CG)法，理论分析显示新算法在多种线搜索条件下具有充分下降性. 进一步证明了新CG算法的全局收敛性定理. 最后，进行了大量数值实验，其结果表明与传统的几类CG方法相比，新算法具有更为高效的计算性能.

关键词: 无约束优化问题, 非线性共轭梯度法, 充分下降性, 全局收敛性

Abstract:

One of the widely used methods for solving large scale unconstrained optimization problems is the conjugate gradient method. In this paper, we propose a new nonlinear conjugate gradient method (CG), which satisfies the sufficient descent condition independent of any line search. We further establish global convergence theorem of the new  CG method. Finally, a large amount of numerical experiments are carried  out  and reported.  It shows that the proposed method has  an efficient computational performance.

Key words: unconstrained optimization, nonlinear conjugate gradient method, sufficient decent condition, global convergence