一种新的非单调谱共轭梯度算法

数学物理学报 ›› 2013, Vol. 33 ›› Issue (1): 78-88.

一种新的非单调谱共轭梯度算法

朝明|万中|王旭

中南大学数学与统计学院长沙 |410083

收稿日期:2011-05-15 修回日期:2012-10-25 出版日期:2013-02-25 发布日期:2013-02-25
基金资助:
国家自然科学基金(71071162, 70921001)资助

A New Nonmonotone Spectral Conjugate Gradient Algorithm

HU Chao-Ming, WAN Zhong, WANG Xu

School of Mathematics and Statistics, Central South University, Changsha 410083

Received:2011-05-15 Revised:2012-10-25 Online:2013-02-25 Published:2013-02-25
Supported by:
国家自然科学基金(71071162, 70921001)资助

摘要/Abstract

摘要：

提出了一类新的非单调谱共轭梯度方法. 该方法通过引入混合因子, 将HS方法和PRP方法结合得到共轭系数的新的选取方式. 以此为基础,通过合适地选取谱系数保证了所有搜索方向不依赖于线搜索条件, 恒为充分下降方向. 其次, 该方法还修正了Zhang和Hager提出的非单调线搜索规则, 在更弱的假设条件下证明了全局收敛性. 数值试验说明了该方法的计算性能优良.

关键词: 谱共轭梯度法, 非单调线搜索, 无约束优化, 全局收敛性

Abstract:

In this paper, a new spectral conjugate gradient method is proposed. By introducing a hybrid coefficient, the conjugacy parameter is determined based on the combination of PRP and HS methods. Then, a spectral parameter is appropriately chosen such that each search direction is a sufficiently descent direction independent of the employed line search techniques. On the other hand, the nonmonotone line search technique proposed by Zhang and Hager is modified, and under more mild assumptions, the global convergence of the developed algorithm is proved. Numerical experiments are employed to demonstrate the efficiency of the algorithm.

Key words: Spectral conjugate gradient method, Nonmonotone line search, Unconstrained optimization, Global convergence

中图分类号:

90C30

胡朝明, 万中, 王旭. 一种新的非单调谱共轭梯度算法[J]. 数学物理学报, 2013, 33(1): 78-88.

HU Chao-Ming, WAN Zhong, WANG Xu. A New Nonmonotone Spectral Conjugate Gradient Algorithm[J]. Acta mathematica scientia,Series A, 2013, 33(1): 78-88.

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