基于修正割线条件的有限记忆BFGS方法  

Limited Memory BFGS Method Based on Modified Secant Condition

作　　者：尹小丽 YIN Xiaoli(College of Mathematics Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《内江师范学院学报》2020年第12期32-36,共5页Journal of Neijiang Normal University

基　　金：重庆市自然科学基金项目(cstc2017jcyjA0788)。

摘　　要：有限记忆BFGS(broyden-fletcher-goldfarb-shanno)方法主要用来求解大规模无约束优化问题,是最有效的拟牛顿方法之一,该方法利用存储一定量的向量对去克服拟牛顿方法需要存储大量矩阵的缺点,同时还保持了良好的收敛性质.通过修正割线条件改进有限记忆BFGS方法,使其具有更好的二阶曲率信息,并证明该方法对一致凸函数具有全局收敛性.与标准有限记忆BFGS方法(limited BFGS,LBFGS)相比,修正有限记忆BFGS方法(modified limited BFGS,MLBFGS)在计算上略有优势.Limited memory BFGS(broyden-fletcher-goldfarb-shanno)method is mainly used to solve large-scale unconstrained optimization problems and is one of the most effective quasi-Newton methods.This method,by utilizing the storage of a certain amount of vector pairs,not only overcomes the shortcomings of the quasi-Newton method(a method needs to store a large number of matrices),but at the same time maintains good convergence property.The method improves the limited memory BFGS method by means of modifying the secant condition to make it acquire a better second-order curvature information,and proves that the method has global convergence for uniformly convex functions.Compared with the standard limited memory BFGS method(LBFGS),the modified limited memory BFGS method(MLBFGS)has a slight advantage in calculation.

关 键 词：有限记忆拟牛顿法 无约束优化 修正割线条件 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]