一种求解无约束优化问题的新混合共轭梯度法  

A New Mixed Conjugate Gradient Method for Solving Unconstrained Optimization Problems

作　　者：唐天国[1] TANG Tian-guo(Department of Electronic Information Engineering, Nanchong Vocational and Technical College, Nanchong Sichuan 637000, China)

机构地区：[1]南充职业技术学院电子信息工程系

出　　处：《西南师范大学学报（自然科学版）》2019年第9期34-39,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：四川省高等职业教育研究中心2016年科研课题(GZY16B09)

摘　　要：在现有共轭梯度方法的基础上,提出一种新混合共轭梯度法来求解无约束最优化问题.该方法采用近似方法去逼近Hessen矩阵,克服了传统牛顿法求解Hessen矩阵中存在的计算量大等问题,并在强wolfe线搜索技术下给出该共轭梯度算法的全局收敛性证明.实验结果表明,与PRP(Polak-Ribiere-Polyak)方法和HYBRID(混合)方法相比较,该文提出的新混合共轭梯度算法的迭代时间少于前两者方法,说明该文方法可行、有效.Based on existing conjugate gradient method, a new conjugate gradient method is proposed to solve the unconstrained optimization problem. An approximate method has been used to approximate the Hessen matrix and to overcome the problem of large computational complexity in the Hessen matrix of traditional Newton method. And under strong Wolfe line search, the global convergence of the conjugate gradient algorithm is proved. The experimental results show that, compared with the PRP(Polak-Ribiere-Polyak) method and HYBRID method based on BFGS(Broyden-Fletcher-Goldfarb-Shanno), the iterative time of the hybrid conjugate gradient algorithm proposed in this paper is less than that of former two methods, which shows that the method is feasible and effective.

关 键 词：共轭梯度法 无约束优化 强Wolfe线搜索 全局收敛性 

分 类 号：O221[理学—运筹学与控制论]