Goldstein线搜索下共轭梯度法的全局收敛性  

Convergence Properties of Conjugate Gradient Methods With Goldstein Line Searches

作　　者：李正锋[1] 陈静 邓乃扬 

机构地区：[1]中国农业大学

出　　处：《中国农业大学学报》1996年第4期15-18,共4页Journal of China Agricultural University

基　　金：国家自然科学基金;北京市自然科学基金

摘　　要：假设目标函数f（x）在水平集上有下界且二次连续可微，证明了带Goldstein线搜索的共轭梯度法产生的搜索方向dk是下降方向，并有。作为一种特殊情形，得到了带Goldstein线搜索的Fletcher－Reeves方法的全局收敛性。Assuming that the objective function f(x) is bounded from below and istwice continuously differentiable on its level set, it is approved that the search directionsgenerated by the conjugate gradient with Goldstein line searches are descent, and. As a special case, the global convergence property of the Fletcher-Reeves method with Goldstein line searches is derived.

关 键 词：共轭梯度法 Goldstein线 线搜索 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]