广义拟牛顿算法对一般目标函数的收敛性  

Global Convergence of the Generalized Quasi-Newton Algorithm for General Objective Functions

作　　者：陈兰平[1] 王丽伟[1] 

机构地区：[1]首都师范大学数学系,北京100037

出　　处：《应用数学》2002年第3期69-75,共7页Mathematica Applicata

基　　金：北京市教委科研基金资助项目 (99KJ10 )

摘　　要：本文证明了求解无约束最优化的广义拟牛顿算法在Goldstein非精确线搜索下对一般目标函数的全局收敛性 ,并在一定条件下证明了算法的局部超线性收敛性 .In this paper,we develop the Generalized Quasi Newton methods for unconstrained optimization which was formed in paper,and we use inexact line searches (Goldstein rule).These methods are globally convergent when applied to a general objective function under the weak condition,and are locally super linearly convergent when applied to a uniformly convex function whoes Hessian matrix G(x) is Lipschitz continuous in the neighborhood of the optimal solution point.So we develop the results of paper and .

关 键 词：无约束最优化 广义拟牛顿算法 Goldstein非精确线搜索 全局收敛 局部超线性收敛性 

分 类 号：O242.23[理学—计算数学]