一种修正的DY共轭梯度法的全局收敛性

Global Convergence for a Modified DY Conjugate Gradient Algorithm

提出了一种新的非线性修正的DY共轭梯度算法(MDYCG),该算法得到的搜索方向为下降方向,它既不受线搜索规则的影响;也不受目标函数的凸性影响;在精确线搜索下,MDYCG算法化归为标准的DY共轭梯度算法;证明了该方法在Armijo型线搜索下的全局收敛性,给出了初步的数值结果。

This paper proposes a kind of new nonlinear modified DY conjugate gradient algorithm, whose search direction is descent direction and which is not affected by line search rule and is not affected by the convexity of objective function either.Under accurate line search, the modified DY conjugate gradient algorithm is turned to standard DY conjugate algorithm. This paper proves the global convergence of this algorithm under Armijotype line search and gives initial numerical result.