Armijo线搜索下谱共轭梯度法全局收敛的一个充分条件

A sufficient condition for global convergence of spectral conjugate gradient methods with Armijo line search

在一般假设下,提出并证明了Armijo线搜索下谱共轭梯度法全局收敛的一个充分条件,分析了充分条件的优越性。分析结果表明:1)该充分条件的一个推论是文献[9]中定理1弱化后的结果;2)谱参数对谱共轭梯度法的全局收敛性起着重要的调节作用;3)该充分条件为构造全局收敛的谱共轭梯度法提供了依据。

Under general assumptions,a sufficient condition for the global convergence of spectral conjugate gradient method with the Armijo line search is put forward and proved,and then the advantages of this sufficient condition are analyzed.The results show that,first,one of the corollaries of this suficient condition is the weakening result of Theorem 1 in Literature 9; second,spectrum parameter plays an important role in regulating the global convergence of spectral conjugate gradient method; third,this sufficient condition provides the basis for constructing spectral conjugate gradient method with global convergence.