一类改进的BFGS拟牛顿法及与其他几种拟牛顿法的比较研究  

A Kind of Improved BFGS Quasi-Newton Method and its Comparison with other Quasi-Newton Methods

作　　者：杨茜 吴泽忠 贺盛瑜 YANG Qian;WU Zezhong;HE Shengyu(College of Applied Mathematics,Chengdu University of Information Technology,Chengdu 610225,China;Xichang University,Xichang 615000,China)

机构地区：[1]成都信息工程大学应用数学学院,四川成都610225 [2]西昌学院,四川西昌615000

出　　处：《成都信息工程大学学报》2023年第2期227-235,共9页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(71962030);四川省社科重点研究基地资助项目(Xq21B06)。

摘　　要：拟牛顿法是最优化中一种重要的求解无约束问题的方法,对拟牛顿算法的改进是一个重点研究内容。基于新拟牛顿方程B_(k+1)·s^((k))=(y^((k)))^(*)提出一个新的改进的BFGS算法,结合以往几种改进的BFGS算法,采用Wolfe线搜索准则对迭代步长进行搜索,并通过选取一些测试函数利用MATLAB工具对这几种改进的BFGS拟牛顿法的收敛效果进行对比分析。实验结果表明,提出的改进的BFGS算法相较于以往几种改进的BFGS算法,收敛效果更好。Quasi-Newton method is an important method to solve unconstrained problems in optimization,and the improvement of the quasi-Newton algorithm is a key research content.In this paper,a new improved BFGS algorithm is proposed based on the new quasi-Newton equation Bk+1·s(k)=(y(k))*.Combined with several previous improved BFGS algorithms,the iterative step size is searched by using the Wolfe line search criterion.By selecting some test functions,the convergence effects of these improved BFGS quasi Newton methods are compared and analyzed by using MATLAB tools.The experimental results show that the improved BFGS algorithm proposed in this paper is an improvement with good convergence effect compared with several previous improved BFGS algorithms.

关 键 词：无约束最优化 BFGS拟牛顿法 拟牛顿方程 Wolfe线搜索准则 

分 类 号：O221.2[理学—运筹学与控制论]