摘要
本文在很弱的条件下得到了关于无约束最优化的Ｐｏｌａｋ—Ｒｉｂｉｅｒｅ和Ｈｅｓｔｅｎｅｓ－Ｓｔｉｅｆｅｌ共轭梯度法的全局收敛性的新结果，这里 ＰＲ方法和ＨＳ方法中的参数β_k^(PR)和β_k^HS可以在某个负的区域内取值，这一负的区域与ｋ有关．这些新的收敛性结果改进了文献中已有的结果．数值检验的结果表明了本文中新的 ＰＲ方法和 ＨＳ方法是相当有效的．
In this paper, some new global convergence results of the Polak-Ribiere and Hestenes Stiefel conjugate gradient methods for unconstrained nonlinear programming problems are obtained under very weak conditions where the parameters and in algorithms can belong to a negative region which is changed depending on k. The results improve some previous convergence results of PR and HS methods. Numerical results show that the methods in this paper are effective.
出处
《运筹学学报》
CSCD
2000年第3期1-7,共7页
Operations Research Transactions
基金
the National Natural Science Foundation of China (grants 19871049 and 19731001)
关键词
无约最优化
全局收敛性
PR共轭梯度法
HS共轭梯度法
Unconstrained optimization
global convergence
PR conjugate gradient method
HS conjugate gradient meth$
