不假定凸性和精确线搜索时DFP算法的收敛性  

Convergence of DFP Algorithms Without Convexity and Exact Line Search Assumptions

作　　者：濮定国[1,2] 刘美玲[3] 

机构地区：[1]同济大学数学系,上海200092 [2]河南科技大学数学系,河南洛阳471003 [3]上海电机学院数理教学部,上海201306

出　　处：《同济大学学报（自然科学版）》2013年第2期289-292,298,共5页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金(10771162;U1135003)

摘　　要：对非凸目标函数,Broyden变尺度算法的收敛性是一个没有完全解决的问题.针对DFP修正公式证明在不假定精确线搜索条件下,对光滑的目标函数,当DFP算法得到的点列收敛时,该点列一定趋向于稳定点.指出对于其他Broyden算法结论都是成立的.The convergence of the Broyden algorithms without convexity and exact line search assumptions is discussed. It is proved that if the objective function is suitably smooth and the DFP algorithm produces a convergence point sequence, then the limit point of the sequence is a critical point of the objective function. We give mainly a proof for the DFP update, then point out that all the results are true for Broyden algorithms by a remark.

关 键 词：变尺度算法 收敛性 凸性 不精确线搜索 

分 类 号：O221.2[理学—运筹学与控制论]