带误差项的FR共轭梯度法及其收敛性  

THE FLETCHER-REEVES CONJUGATE GRADIENT METHOD WITH ERRORS AND ITS CONVERGENCE

作　　者：张劲松[1] 

机构地区：[1]九江学院理学院,九江332005

出　　处：《系统科学与数学》2013年第10期1135-1143,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(71261010)资助课题

摘　　要：在共轭梯度不能精确计算的情况下,研究了带误差项的FR共轭梯度法,因而更适用于许多实际问题.步长规则采用强Wolfe线搜索,在很一般的条件下证明了算法的全局收敛性,并给出了数值实验.结果表明,误差项的出现不影响算法的稳定性.In the case where the conjugate gradient is computed inexactly, we con- sider FR conjugate gradient method with errors, which is more applicable in practice. For the step size rule, the strong Wolfe line search is used, and the global conver- gence of the method is proven under very general conditions. Finally, the numerical experiment results indicate that errors are independent of the stability of algorithm.

关 键 词：共轭梯度法 强Wolfe线搜索 全局收敛性 误差 

分 类 号：O224[理学—运筹学与控制论]