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一个解大规模无约束优化问题的全局梯度法(英文)
引用本文:周群艳,陈俊.一个解大规模无约束优化问题的全局梯度法(英文)[J].应用数学,2012,25(1):202-208.
作者姓名:周群艳  陈俊
作者单位:1. 江苏技术师范学院数理学院,江苏常州,213001
2. 南京晓庄学院数学与信息技术学院,江苏南京,211171
基金项目:Supported by the Jiangsu Teachers University of Technology Foundation(KYY08041)
摘    要:本文提出一种新的解大规模无约束优化问题的全局收敛的梯度法.新算法沿着负梯度方向选择步长,而初始步长根据目标函数的海赛矩阵的近似数量矩阵来确定.理论上证明了新算法产生的点列的每个聚点都是稳定的,数值试验表明新算法是可靠且有效的.

关 键 词:大规模无约束优化  梯度方法  非单调线搜索

A Global Gradient Method for Large Scale Unconstrained Minimization Problems
ZHOU Qunyan , CHEN Jun.A Global Gradient Method for Large Scale Unconstrained Minimization Problems[J].Mathematica Applicata,2012,25(1):202-208.
Authors:ZHOU Qunyan  CHEN Jun
Institution:1.School of Mathematics and Physics,Jiangsu Teachers University of Technology,Changzhou 213001,China;2.School of Mathematics and Information Technology,Nanjing Xiaozhuang University,Nanjing 211171,China)
Abstract:In this paper,a nonmonotone gradient method for large scale unconstrained optimization is proposed.The new algorithm selects the steplength along the negative gradient direction and the initial stepsize is determined using a new scale approximation of the minimizing function’s Hessian.Every limit point of the sequence generated by the new algorithm is proved to be a stationary point of the objective function.Numerical tests on a set of large scale standard test problems are presented and show that the new algorithm is efficient and robust.
Keywords:Large scale unconstrained optimization  Gradient method  Nonmonotone line search
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