修改Broyden非凸族在一般Wolfe搜索下的收敛性  

CONVERGENCE PROPERTIES OF THE PRECONVEX PART OF MODIFIED BROYDEN'S FAMILY WITH A GENERALIZED WOLFE LINESEARCHES

作　　者：韦增欣[1] 谢品杰[1] 顾能柱[1] 

机构地区：[1]广西大学数学与信息科学学院,南宁530004

出　　处：《系统科学与数学》2007年第2期194-207,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10161002);广西自然科学基金(0135004)资助项目.

摘　　要：近来,韦等提出了一类新的拟牛顿方程Bk＋1Sk=yk^＊=yk＋AkSk,Ak为一矩阵,并在此基础上给出了两种类型的修改Broyden族（MBC）．作者利用一般Wolfe搜索技术,与修改Broyden族相结合,证明了在适当的条件下修改Broyden非凸族具有全局收敛性和超线性收敛速度．Recently,Wei and other authors proposed a class of new quasi-Newton equa- tions B_（k＋1）s_k=y_l~＊=y_k＋A_ks_k,where A_k is some matrix,and based on these,they gave two kinds of modified Broyden＇s familes（MBC）.In this paper,generalized Wolfe linesearches proce- dures are used,which are combined with the modified Broyden＇s family.Under some suitable conditions,we prove the global and superlinear convergence property of the preconvex part of the modified Broyden＇s family.

关 键 词：Broyden非凸族 无约束最优化 全局收敛性 超线性收敛性. 

分 类 号：O224[理学—运筹学与控制论]