伪Newton－δ族算法对一般目标函数的收敛性

CONVERGENCE OF THE PSEUDO-NEWTON -δ CLASS METHODS FOR GENERAL OBJECTIVE FUNCTIONS

伪Ｎｅｗｔｏｎ－δ族算法对一般目标函数的收敛性赵云彬（中国科学院应用数学研究所）段虞荣（重庆大学系统科学与工程研究所）ＣＯＮＶＥＲＧＥＮＣＥＯＦＴＨＥＰＳＥＵＤＯ－ＮＥＷＴＯＮ－δＣＬＡＳＳＭＥＴＨＯＤＳＦＯＲＧＥＮＥＲＡＬＯＢＪＥＣＴＩＶＥＦＵＮＣ...

Abstract Pesudo-Newton-δ class methods are new algorithms for unconstrained optimization. If the algorithms use inexact line searches (Goldstein rule), these methods are globally convergent when applied to a general objective function, and are locally super-linearly convergent when applied to a uniformly convex function whose Hessian matrix G (x) is Lipschitz continuous in the neighborhood of the optimal solution.