基于新拟牛顿方程的改进BFGS方法  

Modified BFGS Method Based on the New Quasi-Newton Equation

作　　者：张恒[1] 何伟[2] 

机构地区：[1]淮海工学院数理科学系,江苏连云港222005 [2]南京理工大学数学系,江苏南京210094

出　　处：《淮海工学院学报（自然科学版）》2007年第3期10-12,共3页Journal of Huaihai Institute of Technology:Natural Sciences Edition

摘　　要：针对无约束最优化问题,在已建立的BFGS方法基础上,证明了改进的BFGS方法的收敛性.基于前人的改进的BFGS方法,同时结合有关结论提出一种新的BFGS方法.通过选择适当的参数,证明了改进的BFGS方法对于一类更广的搜索准则保持局部收敛性,在Wolfe搜索准则下方法还具有超线性收敛性.最后通过具体的数值试验结果说明其优越性.A class of modified BFGS method based on the new quasi-Newton equation is presented in this paper to solve the unconstrained optimization problem. We also propose a modified BFGS method based on XIAO＇s modified BFGS method and LIAO＇s modified method. By choosing the proper parameters, we can prove that the new method has global and superlinear convergence properties under suitable conditions. Besides, numerical testing results are given to prove its superiority.

关 键 词：无约束优化 BFGS 全局收敛性 超线性收敛性 

分 类 号：O224[理学—运筹学与控制论]