ON THE CONVERGENCE OF PARALLEL BFGS METHOD

数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (3): 283-294.

ON THE CONVERGENCE OF PARALLEL BFGS METHOD

陈忠¹, 费浦生¹, 周云才²

1. Department of Mathematics, Wuhan University, Wuhan 430072, China;
2. Jianghan Petroleum Institute, Jinsha 434102, China

收稿日期:1993-06-15 修回日期:1993-10-02 出版日期:1995-09-25 发布日期:1995-09-25
基金资助:
Project Supported by National Natural Science Foundation of China.

ON THE CONVERGENCE OF PARALLEL BFGS METHOD

Chen Zhong¹, Fei Pusheng¹, Zhou Yuncai²

1. Department of Mathematics, Wuhan University, Wuhan 430072, China;
2. Jianghan Petroleum Institute, Jinsha 434102, China

Received:1993-06-15 Revised:1993-10-02 Online:1995-09-25 Published:1995-09-25
Supported by:
Project Supported by National Natural Science Foundation of China.

摘要/Abstract

摘要： According to the sequential BFGS method,in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact.We assume that we have p+q processors, which are divided into two groups,the first group has p processors,the second group has q processors,the two groups are asynchronous parallel.If we assume the objective function is twice continuously differentiable and uniformly convex,we prove the iteration converge globally to the solution,and under some additional conditions we show the method is superlinearly convergent.Finally,we show the numerical results of this algorithm.

关键词: BFGS algorithm, superlinear convergence, parallel method

Abstract: According to the sequential BFGS method,in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact.We assume that we have p+q processors, which are divided into two groups,the first group has p processors,the second group has q processors,the two groups are asynchronous parallel.If we assume the objective function is twice continuously differentiable and uniformly convex,we prove the iteration converge globally to the solution,and under some additional conditions we show the method is superlinearly convergent.Finally,we show the numerical results of this algorithm.

Key words: BFGS algorithm, superlinear convergence, parallel method

陈忠, 费浦生, 周云才. ON THE CONVERGENCE OF PARALLEL BFGS METHOD[J]. 数学物理学报(英文版), 1995, 15(3): 283-294.

Chen Zhong, Fei Pusheng, Zhou Yuncai. ON THE CONVERGENCE OF PARALLEL BFGS METHOD[J]. Acta mathematica scientia,Series B, 1995, 15(3): 283-294.

ON THE CONVERGENCE OF PARALLEL BFGS METHOD

ON THE CONVERGENCE OF PARALLEL BFGS METHOD

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