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.
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页码：315 / 332
页数：18
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