一个新的谱共轭梯度法  

A New Spectral Conjugate Gradient Method

作　　者：林穗华[1] 黄海[1] 

机构地区：[1]广西民族师范学院数学与计算机科学系,广西崇左532200

出　　处：《工程数学学报》2014年第6期837-846,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11161003);广西教育厅科研项目(201012MS215;ZD2014143);广西民族师范学院科研项目(2013RCGG002)~~

摘　　要：谱共轭梯度法含有两个方向调控参数,是求解无约束优化问题的一类有效方法.本文给出一对参数公式以构建新的谱共轭梯度法,该方法在精确线搜索下与标准FR方法等价,在Wolfe线搜索下具有类似标准DY方法的内在性质.我们证明了采用Wolfe线搜索的新算法在每一次迭代中均产生下降方向,并且具有全局收敛性.数值实验结果表明,新算法数值稳定、有效,适合于求解大规模无约束优化问题.Spectral conjugate gradient method contains two parameters for direction control, and it is a class of effective algorithms for unconstrained optimization problems. This paper presents a pair of formulas to create a new spectral conjugate gradient method, which is equiv-alent to the standard FR method when the line search is exact, and its intrinsic properties are similar to the standard DY method with Wolfe line search. The descent in each iteration and the global convergence of the new algorithm under Wolfe line search are proved. Preliminary numerical results show that the new algorithm is robust, effective and suitable for solving large-scale unconstrained optimization problems.

关 键 词：无约束优化 谱共轭梯度法 全局收敛 数值试验 

分 类 号：O221.2[理学—运筹学与控制论]