修正Grippo非单调线搜索规则的新对角稀疏拟牛顿算法  

NEW DIAGONAL-SPARSE QUASI-NEWTON METHOD WITH MODIFIED NON-MONOTONE STEP SIZE RULE

作　　者：孙清滢 刘丽敏 王宣战 

机构地区：[1]中国石油大学理学院,东营257061

出　　处：《高等学校计算数学学报》2011年第3期203-214,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(10971118)资助项目;中央高校基本科研业务费专项资金资助(10CX04044A)

摘　　要：1引言 考虑无约束优化问题（P）：inin x∈ R^n f（x）,其中f（x）：R^n→＋R^1是一阶连续可微函数．求解问题（P）的拟牛顿算法收敛速度快，每次迭代不需要计算目标函数的Hesse矩阵及其逆矩阵，We propose a modified non-monotone step size rule and analyze the global convergence of a new diagonal-sparse quasi-Newton method. The new step size rule is similar to the Grippo non-monotone step size rule and contains it as a special case. We can choose a larger stepsize in each line search procedure and main- tain the global convergence property of our diagonal-sparse quasi-Newton method under the assumption that Vf（x） is uniformly continuous, and further analyze the superlinear convergence property of the new method. Numerical results show that the new algorithm is efficient and suitable to solve large scale problems.

关 键 词：拟牛顿算法 搜索规则 无约束优化问题 HESSE矩阵 稀疏 调线 连续可微函数 收敛速度 

分 类 号：O221.2[理学—运筹学与控制论]