曲线搜索下记忆梯度法的收敛性  

CONVERGENE OF MEMORY GRADIENT METHOD WITH CURVE SEARCH RULE

作　　者：汤京永[1,2] 贺国平[3] 

机构地区：[1]信阳师范学院数学与信息科学学院,信阳464000 [2]上海交通大学数学系,上海200240 [3]山东科技大学信息科学与工程学院,青岛266510

出　　处：《高等学校计算数学学报》2012年第4期308-315,共8页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(10571109;10971122);山东省自然科学基金(Y2008A01);高等学校博士学科点专项科研基金(200937181 10005)

摘　　要：1 引言 考虑无约束优化问题（UP）： min f（x），x∈R^n,In this paper, we present a new memory gradient method for uncon- strained optimization problems. The global convergence and linear convergence rate are proved under some mild conditions. At each iteration, the new iterative point is determined by means of a curve search rule that resembles Armijo＇s lin- ear search rule. It is particular that the search direction and the step-size are determined simultaneously at each iteration. The method, similarly to conjugate gradient methods, avoids the computation and storage of some matrices associated with the Hessian of objective functions. It is suitable to solve large scale minimiza- tion problems. Numerical results show. that the new method is efficient in practical computation.

关 键 词：记忆梯度法 曲线搜索 收敛性 无约束优化问题 R^N 

分 类 号：O221.2[理学—运筹学与控制论]