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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (6): 16-23.doi: 10.6040/j.issn.1671-9352.0.2015.267

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建立在DY法上的两类混合共轭梯度法

王开荣1,高佩婷2   

  1. 重庆大学数学与统计学院, 重庆 401331
  • 收稿日期:2015-06-01 出版日期:2016-06-20 发布日期:2016-06-15
  • 作者简介:王开荣(1965— ),男,教授,博士,研究方向为最优化理论及算法. E-mail: kairong@cqu.edu.cn
  • 基金资助:
    重庆市研究生教育教学改革研究项目(yjg143046)

Two mixed conjugate gradient methods based on DY

WANG Kai-rong1, GAO Pei-ting2   

  1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
  • Received:2015-06-01 Online:2016-06-20 Published:2016-06-15

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摘要： 在经典的DY共轭梯度法的基础上,提出了两种混合共轭梯度,并证明了在特定的条件下,这两种算法所产生的方向均为充分下降方向,同时在广义Wolfe线搜索条件下,这两种方法又具有全局收敛性。数值试验结果表明新方法对于给定的测试函数在数值效果上明显优于DY共轭梯度法。

关键词: Wolfe线搜索, 无约束最优化问题, 充分下降性, 全局收敛性, 共轭梯度法

Abstract: Based on DY method, two mixed conjugate gradient methods(GDY1 and GDY2)were proposed. The search directions generated by GDY1 and GDY2 are sufficiently decent directions under some specific conditions, and are global convergence with general wolf line search. Numerical experiments show that the new methods outperform DY conjugate gradient method.

Key words: unconstrained optimization, conjugate gradient methods, sufficiently descent property, Wolfe line searching, global convergence

中图分类号: 

  • O221.2
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