求解大规模优化的混合共轭梯度法  

A Mixed Conjugate Gradient Method for Large Scale Problems

作　　者：曹名圆[1] 杨月婷[1] 

机构地区：[1]北华大学数学学院,吉林132013

出　　处：《工程数学学报》2013年第1期10-18,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11171003);教育部科学技术重点项目(211039);吉林省自然科学基金(201215102)~~

摘　　要：为了有效求解大规模无约束优化问题,在PRP方法和FR方法的基础上,给出了满足共轭条件的新的混合共轭梯度法.在强Wolfe线性搜索下,证明了此算法的全局收敛性.在特定条件下,新公式与HS公式一致,因此可看作是对HS方法的修正.对7个经典无约束优化问题的数值实验结果表明,所提出的新方法数值稳定.相比已有方法,随着问题规模的增大,所提方法在迭代次数,优化精度及梯度调用次数方面表现出明显优势.Based on the PRP and FR methods, a new mixed conjugate gradient method is presented. The new method satisfies the conjugate condition so that it can effectively solve the large scale unconstrained optimization. The global convergence of the method is proved with the strong Wolfe line search. Under certain conditions, the new formula is proved to be consistent to that of HS, and hence the new method can be regarded as a modified version of HS. The numerical results on 7 classical unconstrained optimization problems substantiate that the proposed method is robust and outperforms the previous methods in terms of iteration times, accuracy and gradient call frequency. These advantages of the proposed method is more prominent in large scale optimization problems.

关 键 词：无约束优化 混合共轭梯度法 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]