THE CONVERGENCE OF BROYDEN ALGORITHMS FOR LC GRADIENT FUNCTION

被引：1

作者：

濮定国

机构：

来源：

Acta Mathematicae Applicatae Sinica(English Series) | 2000年 / 03期

关键词：

Variable metric algorithms; convex; convergence; convergence rate;

D O I：

暂无

中图分类号：

O241 [数值分析];

学科分类号：

070102 ;

摘要：

In this paper, we discuss the convergence of Broyden algorithms for the functions which are non-twice differentiable, but have LC gradient. We prove that the rate of convergence of the algorithms is linear for uniformly convex functions. We also demonstrate that under some mild conditions the algorithms are superlinsarly convergent.

引用

页码：313 / 319

页数：7

共 6 条

[1] 一类带非精确线搜索的修改的Broyden算法 [J].

濮定国，田蔚文 .

高校应用数学学报A辑(中文版), 1995, (03) :313-322

[2]

A CLASS OF MODIFIED BROYDEN ALGORITHMS[J]. Pu Ding-guo(Department of Mathematics, Shanghai Institute of Railway Technology, Shanghai, China)Tian Wei-wen(Department of Mathematics, Shanghai University of Science and Technology, China).Journal of Computational Mathematics. 1994(04)

[3]

On the convergence property of the DFP algorithm[J] . Dingguo Pu,Wenci Yu.Annals of Operations Research . 1990 (1)

[4] GLOBAL CONVERGENCE OF A CLASS OF QUASI-NEWTON METHODS ON CONVEX PROBLEMS [J].

BYRD, RH ;

NOCEDAL, J ;

YUAN, YX .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (05) :1171-1190

[5]

Variable metric algorithms: Necessary and sufficient conditions for identical behavior of nonquadratic functions[J] . L. C. W. Dixon.Journal of Optimization Theory and Applications . 1972 (1)

[6]

Optimization and nonsmooth analysis. FH Clarke. . 1990

← 1 →