基于Armijo搜索步长的BFGS与DFP拟牛顿法的比较研究  

Comparison of BFGS and DFP Quasi-Newton Method based on Armijo Search Step

作　　者：李菊雯 吴泽忠 LI Juwen;WU Zezhong(College of Applied Mathematics,Chengdu University of Information Technology,Chengdu 610225,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

出　　处：《成都信息工程大学学报》2021年第5期558-563,共6页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(71672013)。

摘　　要：拟牛顿法是求解无约束优化问题的重要方法,采用非精确Armijo准则确认搜索步长,其中初始点的选取采用两种不同的方法:利用MATLAB工具箱中的rand命令对BFGS和DFP两种算法的初始点进行随机选取;固定选择两个不同的初始点。讨论不同的初始点选取方法对两种算法收敛效率及结果的影响,最后对两种算法收敛效果进行比较研究。结果表明:在多项式函数中,初始点的选取方法对DFP法的收敛效率有一定影响,在低次函数中,DFP法收敛效率更好,在高次函数中,使用BFGS法的收敛效果更好;在非多项式函数中,随机取点对计算结果有一定影响,选择离极小点近的点作为初始点得到的最小值更好,并且使用BFGS法的收敛速度更快。Quasi-Newton method is an important method to solve unconstrained optimization problems.In this paper,an inexact Armijo criterion is used to confirm the search step size,and two different methods are used to select the initial points:one is to use the rand command in MATLAB toolbox to randomly select the initial points of BFGS and DFP algorithms;the other is to select two different initial points fixedly.The influence of different initial point selection methods on the convergence efficiency and results of the two algorithms is discussed.Finally,the convergence effect of the two algorithms is compared.The results show that in polynomial function,the selection method of initial point has certain influence on the convergence efficiency of DFP method.In lower order function,DFP method has better convergence efficiency.And in higher order function,BFGS method has better convergence effect.In the non-polynomial function,the random selection of points has a certain influence on the calculation results.It is better to select the point near the minimum point as the initial point,and the BFGS method has faster convergence speed.

关 键 词：无约束最优化 BFGS拟牛顿法 DFP拟牛顿法 ARMIJO搜索 

分 类 号：O221.2[理学—运筹学与控制论]