具有充分下降性的修正型混合共轭梯度法

J4 ›› 2013, Vol. 48 ›› Issue (09): 78-84.

具有充分下降性的修正型混合共轭梯度法

王开荣,王书敏

重庆大学数学与统计学院, 重庆 401331

收稿日期:2013-03-29 出版日期:2013-09-20 发布日期:2013-09-25
作者简介:王开荣(1965- ),男,教授,博士,主要从事最优化理论及算法的研究. Email:kairong@cqu.edu.cn
基金资助:
重庆市高等教育教学改革研究重点项目(102104)

The modified hybrid conjugates gradient methods with sufficient descent property

WANG Kai-rong, WANG Shu-min

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received:2013-03-29 Online:2013-09-20 Published:2013-09-25

摘要/Abstract

摘要：

基于已有的共轭梯度法思想,分别对两种混合共轭梯度法的搜索方向进行修正,使得新的修正型混合共轭梯度法在每步迭代都不依赖于任何线搜索而自行产生充分下降方向。在适当的条件下,证明了新算法在Wolfe线搜索下的全局收敛性。数值实验表明该方法是有效的。

关键词: 无约束优化;共轭梯度法;充分下降性;全局收敛性

Abstract:

With the existing conjugate gradient method, the search directions of two hybrid conjugate gradient methods were modified, such that the new hybrid conjugate gradient methods can automatically generate sufficient descent direction independent of the line search used for each iteration. Under appropriate conditions and the Wolfe line search, it was proved that the new methods are globally convergent. Preliminary numerical results show that the methods are efficient.

Key words: unconstrained optimization; conjugate gradient methods; sufficient descent property; global convergence

王开荣,王书敏. 具有充分下降性的修正型混合共轭梯度法[J]. J4, 2013, 48(09): 78-84.

WANG Kai-rong, WANG Shu-min. The modified hybrid conjugates gradient methods with sufficient descent property[J]. J4, 2013, 48(09): 78-84.

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