一种基于正则化模型的Dai-Liao共轭梯度法  

A Dai-Liao Conjugate Gradient Method Based on Regularization Model

作　　者：倪艳 刘泽显 陈炫睿 NI Yan;LIU Zexian;CHEN Xuanrui(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵阳550025

出　　处：《吉林大学学报（理学版）》2024年第3期529-537,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12261029);贵州省自然科学基金一般项目(批准号:黔科合基础-ZK[2022]一般084).

摘　　要：给出一种基于正则化模型的Dai-Liao共轭梯度法.首先,通过极小化3次正则化模型,得到新的Dai-Liao参数t,并在此基础上根据函数在迭代点附近的性质,产生一个自适应的Dai-Liao参数;其次,结合改进的Wolfe线搜索,提出一种基于正则化模型的Dai-Liao共轭梯度法;最后,证明该算法的搜索方向满足充分下降性,并在一般假设下建立该算法的全局收敛性.数值结果表明该算法有效.We gave a Dai-Liao conjugate gradient method based on regularization model.Firstly,a new Dai-Liao parameter t was obtained by minimizing the 3-degree regularization model,and based on this,an adaptive Dai-Liao parameter was generated according to the properties of the function near the iterative point.Secondly,combined with improved Wolfe line search,we proposed a Dai-Liao conjugate gradient method based on regularization model.Finally,we proved that the search direction of the proposed method satisfied sufficient descent,and established the global convergence of the proposed algorithm under the general assumption.Numerical results show that the proposed algorithm is effective.

关 键 词：共轭梯度法 正则化模型 Dai-Liao共轭参数 充分下降性 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]