求解无约束优化问题的Aitken加速算法  

An Aitken acceleration iteration method for solving unconstrained optimization problem

作　　者：谢亚君 姚洁[1] 马昌凤 XIE Ya-Jun;YAO Jie;MA Chang-Feng(School of Technology,Fuzhou University of International Studies and Trade,Fuzhou 350202,China;College of Mathematics and Informatics,Fujian Normal University,Fuzhou 350007,China)

机构地区：[1]福州外语外贸学院理工学院,福建福州350202 [2]福建师范大学数学与信息学院,福建福州350007

出　　处：《高校应用数学学报（A辑）》2021年第4期481-491,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：福建省自然科学基金(2019J01879);福州外语外贸学院高层次人才计划(FWKQJ202002);国科大实验室技术合作研发项目(20A01246ZY,H2020003)。

摘　　要：拟牛顿法是求解无约束优化问题的经典且有效方法.基于Neculai(2019)提出的所谓对角拟牛顿更新技巧,构造了一种新的修正Aitken加速算法来求解无约束优化问题.理论上保证了该方法相比于对角拟牛顿更新技巧有更高阶的收敛性能.数值测试结果也验证了所提出算法的高效性.Quasi-Newton iteration is a class of popular method for unconstrained optimization problem.In this research,based on so-called diagonal quasi-Newton updating method proposed by Neculai(2019),a modified Aitken acceleration approach is firstly investigated to solve unconstrained optimization problem.The performance is ensured theoretically at least higher-order rate of convergence in comparison to diagonal quasi-Newton updating method.Numerical experiments illustrate the efficiency of the proposed method.

关 键 词：无约束优化问题 修正Aitken加速迭代 高阶收敛性 数值实验 

分 类 号：O224.2[理学—运筹学与控制论]