一类拟牛顿算法的收敛性  

Convergence Properties of a Class of Quasi-Newton Algorithm

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,广西南宁530004

出　　处：《广西科学》2006年第4期282-287,292,共7页Guangxi Sciences

基　　金：国家自然科学基金(No.10161002);广西自然科学基金项目(No.0135004)资助

摘　　要：根据一类基于新拟牛顿方程Bk+1sk=yk*的修改BFGS类算法,采用广义W olfe线搜索模型(GW搜索模型):f(xk+1)≤f(xk)+δkαgTkdk和g(xk+1)Tdk≥m ax{,σ1-(kα‖dk‖)p}gTkdk,其中0<δ≤σ<1,p∈(-∞,1),得到一类修正的BFGS算法(M BFGS),证明了M BFGS算法的全局收敛性和超线性收敛性.数值试验结果表明M BFGS算法是有效的.In this paper, we present a modified BFGS method, which satisfies the quasi-Newton funtion proposed by Wei. Under suitable conditions, we establish global convergence and superlinear convergence for our algorithm with the general Wolfe line search. The numerical results are also presented, which show that the proposed algorithm is efficient for unconstrained optimization problems.

关 键 词：无约束优化 BFGS算法 全局收敛性 超线性收敛性 

分 类 号：O242.23[理学—计算数学]