改进的PSB拟牛顿修正矩阵的收敛性

Convergence of Modified Quasi-Newton Matrice Generated by PSB Update

本文在已建立的一类新拟牛顿方程 Bk+1 δk=yk=yk+ θkδTkuu的基础上 ,证明了满足新拟牛顿方程的改进 PSB算法产生的拟牛顿修正矩阵序列在序列 {xk}收敛于x* ,{δk}一致线性无关及二阶导数阵连续有界的条件下收敛于海色阵 G( x* )

Based on the modified quasi Newton equation B k+1 δ k= k=y k+θ kδ T kuu, it is proved in this paper that the sequence of quasi Newton matrices B k generated by the PSB updating converges to the true Hessian matrix G(x *) under the assumptions that the sequence {x k} converges to x *,{δ k} is uniformly linearly independent and the second derivatives of f(x) is continuous and bounded.