一类共轭梯度法的全局收敛性结果(英文)

A Global Convergence Result of a Class of Conjugate Gradient M ethod

本文证明了在Grippo Lucidi线搜索下当 βk 取βk=σ1 βPRPk +σ2 βnewk ,其中σ1 ≥ 0 ,σ2≥ 0 ,σ1 +σ2 >0 ,βnewk =gTk( gk-gk- 1 )-dTk - 1 gk - 1时一类共轭梯度法的全局收敛性 。

In this paper,we prove a global convergenc e o f a class of conjugate gradient method with GrippoLucidi linesearch and β k satisfies β k=σ 1β PRP k+σ 2β new k where σ 1≥0,σ 2≥0,σ 1+σ 2>0,β new k=g T k(g k-g k- 1 )-d T k-1 g k-1 .Good numerical results of this cla ss of conjugate gradient method are also given.