非单调共轭梯度法的全局收敛结果

Global Convergence Result For Nonmonotone Conjugate Gradient Methods

共轭梯度法主要依靠d1=-g1,dk+1=-gk+1+βkdk,k 1,其中g为目标函数f(x)的梯度,进行迭代,不同的βk会产生不同的算法.本文主要是在非单调线搜索的条件下,当βk满足σ|βk/βFRk| σ(0<σ<1,0< σ<12)时证明了其全局收敛性.

Conjugate gradient method mainly depend on the search directions d1=g1,dk+1=-gk+1+βkdk,k1,where g is the gradient of f(x).Diffierent algorithms arise from different βk. A global convergence is proved under a nonmonotone line search and βk satified σ|βk/βF Rk| where 0<σ<1,0<<12. 