一种新型线搜索下的修正3项LS谱共轭梯度法  

A modified three terms LS conjugate gradient method with a new line search

作　　者：王松华 黎勇 吴加其 WANG Songhua;LI Yong;WU Jiaqi(College of Mathematics and Statistics Science,Baise University,Baise 533000,China;College of Mathematics and Information Science,Guangxi University,Nanning 530004,China)

机构地区：[1]百色学院数学与统计学院,广西百色533000 [2]广西大学数学与信息科学学院,广西南宁530004

出　　处：《安徽大学学报（自然科学版）》2019年第4期40-44,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11661001,11661009);广西自然科学基金资助项目(AD2014132);广西自然科学青年基金资助项目(2014GXNSFBA118283);广西教育厅科研资助项目(YB2014389,YB2014381)

摘　　要：基于经典非线性谱共轭梯度法和3项共轭梯度法,在Yuan等提出修正3项PRP共轭梯度法的基础上,提出了一种求解大规模无约束优化问题的非线性修正3项LS谱共轭梯度法.该方法不依赖任何线搜索,具有充分下降性.在适当条件下,新方法在Yuan等提出的新型非精确线搜索下具有全局收敛性.初步的数值试验结果表明,新方法对给定的测试函数是有效和稳定的,比传统LS方法和3项LS方法更有效。Based on the classical nonlinear spectral conjugate gradient method,the three-term conjugate gradient method,and the modification of the three-term PRP conjugate gradient method proposed by Yuan et al.,a nonlinear modified three-term LS spectral conjugate gradient method for large-scale unconstrained optimization problems was proposed. This method did not depend on any line search and has sufficient descent property. Under appropriate conditions,the new method had global convergence under the new inexact line search proposed by Yuan et al. Preliminary numerical experiments showed that the new method was effective and stable for given test functions,and was more effective than the traditional LS method and three LS methods function.

关 键 词：无约束优化 共轭梯度法 非精确线搜索 充分下降性 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]