扩展的拟牛顿法  

The extended quasi-Newton methods

作　　者：刘伟[1] 张兰[2] 赵陆一 

机构地区：[1]西北大学数学系,陕西西安710127 [2]西安航空职业技术学院基础部,陕西西安710089 [3]陕西省生产力促进中心,陕西西安710054

出　　处：《纺织高校基础科学学报》2008年第4期487-491,共5页Basic Sciences Journal of Textile Universities

摘　　要：拟牛顿算法被认为是当今解无约束最优化问题的最有效方法之一,它产生了一系列对目标函数二阶导数的近似矩阵Bk+1.校正产生的Bk+1其实质是在Bk的基础上加一修正矩阵Ak,即Bk+1=Bk+Ak.研究了Ak应满足什么样的条件,给出了满足该条件的Ak的3种公式及6种合适的选取.One of effective methods for solving the contemporary unconstrained optimization problems is Quasi-Newton methods which produce a series of matrix Bk＋1 for the approx-imation matrix of second order derivatives of the objective function. The nature of Bk＋1 is Bk＋1= Bk＋Ak, in which Bk is the approximation matrix at the last iteration, Ak is some matrix. What conditions Ak can satisfy is studied. Three formulaes and six reasonable choices of Ak based on the conditions are given.

关 键 词：无约束优化 拟牛顿方程 全局收敛性 

分 类 号：O242.2[理学—计算数学]