广义Armijo步长搜索下循环共轭方向算法的收敛性证明

The Convergence Proof on Conjugate Directions Algorithm with Generalized Armijo Steplength Search

共扼方向算法中搜索方向依赖于对参数β（ｋ）的选取ｓ（１）＝－ｇ（１）ｓ（ｋ＋１）＝－ｇ（ｋ＋１）＋β（ｋ）ｓ（ｋ），ｋ≥１．本文给β（ｋ）适当条件以保证算法的下降性，并在广义Ａｒｍｉｊｏ步长搜索下，给出了算法的收敛性证明．

In the conjugate direction algorithm, search direction is dependent onthe selection of parameter β^(k): s^(1) = g^(1), s^(k+1)=-g^(k+1)+β^(k)s^(k),k≥1. The conver-gence proof of algorithm under generalized Armijo steplength search and ensuring thedescene of algorithm is given.