数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 214-228.doi: 10.1007/s10473-019-0117-6

• 论文 • 上一篇    下一篇

NEW HYBRID CONJUGATE GRADIENT METHOD AS A CONVEX COMBINATION OF LS AND FR METHODS

Snežana S. DJORDJEVIĆ   

  1. Faculty of Technology, University of Nis, 16000 Leskovac, Serbia
  • 收稿日期:2017-05-23 修回日期:2018-04-29 出版日期:2019-02-25 发布日期:2019-11-14
  • 作者简介:Snezana S. DJORDJEVIC;,E-mail:snezanadjordjevic1971@gmail.com,snezanadjordjevicle@gmail.com

NEW HYBRID CONJUGATE GRADIENT METHOD AS A CONVEX COMBINATION OF LS AND FR METHODS

Snežana S. DJORDJEVIĆ   

  1. Faculty of Technology, University of Nis, 16000 Leskovac, Serbia
  • Received:2017-05-23 Revised:2018-04-29 Online:2019-02-25 Published:2019-11-14

摘要: In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Furthermore, this property doesn’t depend on any line search. Next, we also prove that, moduling the value of the parameter t, the Newton direction condition is equivalent to Dai-Liao conjugacy condition.The strong Wolfe line search conditions are used.
The global convergence of this new method is proved.
Numerical comparisons show that the present hybrid conjugate gradient algorithm is the efficient one.

关键词: hybrid conjugate gradient method, convex combination, Dai-Liao conjugacy condition, Newton direction

Abstract: In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Furthermore, this property doesn’t depend on any line search. Next, we also prove that, moduling the value of the parameter t, the Newton direction condition is equivalent to Dai-Liao conjugacy condition.The strong Wolfe line search conditions are used.
The global convergence of this new method is proved.
Numerical comparisons show that the present hybrid conjugate gradient algorithm is the efficient one.

Key words: hybrid conjugate gradient method, convex combination, Dai-Liao conjugacy condition, Newton direction