The superlinear convergence of a modified BFGS-type method for unconstrained optimization

被引：114

作者：

Wei, ZX ^{[1
]}

Yu, GH ^{[1
]}

Yuan, GL ^{[1
]}

Lian, ZG ^{[1
]}

机构：

[1] Guangxi Univ, Dept Math & Informat Sci, Nanning 530004, Guangxi, Peoples R China

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2004年 / 29卷 / 03期

关键词：

unconstrained optimization; quasi-Newton method; superlinear convergence;

D O I：

10.1023/B:COAP.0000044184.25410.39

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The BFGS method is the most effective of the quasi-Newton methods for solving unconstrained optimization problems. Wei, Li, and Qi [6] have proposed some modified BFGS methods based on the new quasi-Newton equation B(k+1)s(k)=y(k)*, where y(k)* is the sum of y(k) and A(k)s(k), and A(k) is some matrix. The average performance of Algorithm 4.3 in [16] is better than that of the BFGS method, but its superlinear convergence is still open. This article proves the superlinear convergence of Algorithm 4.3 under some suitable conditions.

引用

页码：315 / 332

页数：18

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