一种具有充分下降性的LS型三项共轭梯度法  

A LS-type Three-term Conjugate Gradient Method with Sufficient Descent Property

作　　者：宋丹 江羡珍 刘鹏杰 SONG Dan;JIANG Xian-zhen;LIU Peng-jie(College of Mathematics and Physics,Guangxi University for Nationalities,Nanning 530006,China;College of Mathematics and Information Science,Guangxi University,Nanning 530004,China)

机构地区：[1]广西民族大学数学与物理学院,广西南宁530006 [2]广西大学数学与信息科学学院,广西南宁530004

出　　处：《数学的实践与认识》2021年第16期207-215,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11771383);广西自然科学基金(2020GXNSFDA238017);广西民族大学科研基金(2018KJQD02);广西民族大学研究生创新项目(gxun-chxzs2019034)。

摘　　要：三项共轭梯度法作为二项共轭梯度法的一种拓展形式,亦是求解大规模无约束问题的有效方法之一.通过构造一个新的共轭参数与三项参数,并在某一限制条件下选择最速下降方向作为重启方向,进而建立了一种新的修正LS型三项共轭梯度算法.使用强Wolfe非精确线搜索产生步长时,证明了新算法具有充分下降性与全局收敛性.最后,对算法进行数值试验并与当前数值效果较好的同类方法进行比较,结果表明新算法是有效的.As an extension of conjugate gradient method,the three-term conjugate gradient method is also one of the effective methods for solving large-scale unconstrained problems.In this paper,a LS type conjugate gradient method is obtained by constructing a new conjugate parameter and three parameters.In addition,A new modified LS type three-term conjugate gradient algorithm is proposed by selecting the fastest descending direction as the restarting direction under a certain restriction condition.When using the strong Wolfe inexact line search to generate the step length,proved that the sufficient descent property and global convergence of the algorithm.Finally,the numerical experiments results of the new algorithm show that the algorithm is robust and effective.

关 键 词：无约束优化 三项共轭梯度法 强Wolfe线搜索 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]