ADAPTIVE REGULARIZED QUASI-NEWTON METHOD USING INEXACT FIRST-ORDER INFORMATION  

作　　者：Hongzheng Ruan Weihong Yang 

机构地区：[1]School of Mathematical Sciences,Fudan University,Shanghai 200433,P.R.China

出　　处：《Journal of Computational Mathematics》2024年第6期1656-1687,共32页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.NSFC-11971118).

摘　　要：Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and its gradient.It is necessary to design optimization algorithms that can utilize inexact first-order information.In this paper,we propose an adaptive regularized quasi-Newton method to solve such problems.Under some mild conditions,we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method.Detailed implementations of our method,including the subspace technique to reduce the amount of computation,are presented.Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method,which can utilize the inexact first-order information effectively.

关 键 词：Inexact first-order information REGULARIZATION Quasi-Newton method 

分 类 号：O17[理学—数学]