华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (1): 44-51.

• 应用数学与基础数学 • 上一篇    下一篇

一种新的修正 Liu-Storey 共轭梯度法的全局收敛性（英）

曹伟,王开荣   

  1. 重庆大学 数理学院,重庆 400030
  • 收稿日期:2009-04-21 修回日期:2009-06-18 出版日期:2010-01-25 发布日期:2010-01-25
  • 通讯作者: 王开荣

Global convergence of a new conjugate gradient method for modified Liu-Storey formula

CAO Wei, WANG Kai-rong   

  1. College of Mathematics and Physics, Chongqing University, Chongqing 400030, China
  • Received:2009-04-21 Revised:2009-06-18 Online:2010-01-25 Published:2010-01-25
  • Contact: WANG Kai-rong

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摘要： 在 Liu-Storey(LS)公式的基础上给出了一个修正的共轭梯度公式 beta _k^MLS. 证明了该新公式在 Wolfe-Powell 线搜索下, 甚至在强 Wolfe-Powell 线搜索下, 在满足sigma in bigg(0,textstyle1 over 2bigg) 的同时, 新算法具有充分下降性和全局收敛性. 数值结果展现了算法的可行性.

关键词: 无约束优化, 共轭梯度法, SWP线搜索, 全局收敛性, 无约束优化, 共轭梯度法, SWP线搜索, 全局收敛性

Abstract: In this paper, a modified conjugate gradient formula beta _k^MLSbased on the formula of the Liu-Storey(LS) nonlinear conjugate gradient method was proposed. It was proved that under the Wolfe-Powell line search and even under the strong Wolfe-Powell line search, with parameter sigma in bigg(0,frac12bigg), the new method has sufficient descent and global convergence properties. Preliminary numerical results show that the method is very promising.

Key words: conjugate gradient method, SWP line search, global convergence, unconstrained optimization, conjugate gradient method, SWP line search, global convergence

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