一种三项CD共轭梯度法及其全局收敛性

A Three- term CD Conjugate Gradient Method and Its Global Convergence

在前人提出的三项PRP共轭梯度法的基础上,提出了一种三项CD共轭梯度法.与以往求解无约束优化问题的经典二项共轭梯度法不同,该算法的搜索方向是三项的,且在任何线性搜索下都具有充分下降性.在适当的条件下,证明了三项CD共轭梯度法在强Wolfe线性搜索下具有全局收敛性.

Based on a three -term PRP conjugate gradient method proposed by other scholars,we present a three -term CD conjugate gradient method in this paper.It is different than classical two -term conjugate gradient method for unconstrained optimization prob-lems.The direction generated by the method is always a descent direction.And this property is independent of the line search used. Under appropriate conditions,we show that the three -term CD conjugate gradient method with strong Wolfe line search is globally con-vergent.