Wolfe线搜下改进的FR型谱共轭梯度法  

FR Type Spectral Conjugate Gradient Method Improved by Wolfe Line-search

作　　者：王森森 韩信 吴祥标 WANG Sen-sen;HAN Xin;WU Xiang-biao(School of Mathematics and Information Science,Xinjiang Hetian College,Hetian 848000,China;School of Mathematics,Sichuan University of Arts and Sciences,Dazhou 635000,China;School of Mathematics,Zunyi Normal University,Zunyi 563006,China)

机构地区：[1]新疆和田学院数理学院,新疆维吾尔自治区和田市848000 [2]四川文理学院数学学院,四川达州635000 [3]遵义师范学院数学学院,贵州遵义563006

出　　处：《遵义师范学院学报》2024年第5期80-84,共5页Journal of Zunyi Normal University

基　　金：达州市社科联重点平台数学与金融研究中心资助项目一般项目(SCMF202206);政务数据安全达州市重点实验室一般项目(ZSAQ202311)。

摘　　要：谱共轭梯度法作为经典共轭梯度法的推广,它是求解大规模无约束优化问题的有效方法之一.基于标准Wolfe线搜索准则和充分下降性条件,提出了一种具有充分下降性质的FR型谱共轭梯度法.在温和的假设条件下,该算法具有全局收敛性.最后,将新算法与现存的修正FR型谱共轭梯度法进行比较,数值结果表明提出的算法是极其有效的.The spectral conjugate gradient method,as an extension of the classical conjugate gradient method,is one of the effective methods for solving large-scale unconstrained optimization problems.Based on the standard Wolfe line search criterion and sufficient descent condition,a FR type spectral conjugate gradient method with sufficient descent property is proposed.Under mild assumptions,the algorithmhas global convergence.Finally,the new algorithmis compared with the existing modified FR type spectral conjugate gradient method,and numerical results show that the proposed algorithm is extremely effective.

关 键 词：无约束优化 谱共轭梯度法 充分下降性 标准Wolfe线搜索准则 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]