On the global convergence of the BFGS method or nonconvex unconstrained optimization problems

被引：174

作者：

Li, DH ^{[1
]}

Fukushima, M

机构：

[1] Hunan Univ, Dept Appl Math, Changsha 410082, Peoples R China

[2] Kyoto Univ, Grad Sch Informat, Dept Appl Math & Phys, Kyoto 6068501, Japan

来源：

SIAM JOURNAL ON OPTIMIZATION | 2001年 / 11卷 / 04期

关键词：

unconstrained optimization; BFGS method; global convergence;

D O I：

10.1137/S1052623499354242

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the open problem of whether the BFGS method with inexact line search converges globally when applied to nonconvex unconstrained optimization problems. We propose a cautious BFGS update and prove that the method with either a Wolfe-type or an Armijo-type line search converges globally if the function to be minimized has Lipschitz continuous gradients.

引用

页码：1054 / 1064

页数：11

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