具有充分下降性的改进FR共轭梯度法  

THE IMPROVED FR CONJUGATE GRADIENT METHOD WITH SUFFICIENT DESCENT PROPERTY

作　　者：马国栋 江羡珍 靳文慧 MA Guo-dong;JIANG Xian-zhen;JIN Wen-hui(College of Mathematics and Physics,Guangxi University for Nationalities,Nanning Guangxi 530006)

机构地区：[1]广西民族大学数学与物理学院,广西南宁530006

出　　处：《数学杂志》2021年第3期212-218,共7页Journal of Mathematics

基　　金：广西自然科学基金资助(2018GXNSFAA281099);国家自然科学基金资助(11771383).

摘　　要：本文研究了大规模无约束优化问题,提出了一个基于改进的FR共轭参数公式的共轭梯度法.不依赖于任何线搜索准则,算法所产生的搜索方向总是充分下降的.在标准Wolfe线搜索准则下,获得了新算法的全局收敛性.最后,对所提出的算法进行了初步数值实验,其结果表明所改进的方法是有效的.In this paper,we consider solving large-scale unconstrained optimization,based on the improved parameter formula of the FR method,a conjugate gradient method that is proposed.Without any line search,we proved that the search direction always satisfied sufficient descent condition at each iteration.The global convergence of the proposed method is proved under the standard Wolfe inexact line search condition.Finally,some elementary numerical experiments are reported,which show that the algorithm is promising.

关 键 词：无约束优化 共轭梯度法 标准Wolfe线搜索 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]