一类新的曲线搜索下的记忆梯度法(英文)  

A New Class of Memory Gradient Method with Curve Search Rule

作　　者：汤京永[1,2] 董丽[1] 

机构地区：[1]信阳师范学院数学与信息科学学院,河南信阳464000 [2]上海交通大学数学系,上海200240

出　　处：《应用数学》2010年第3期575-581,共7页Mathematica Applicata

基　　金：Supported by NSF of China(10571109)

摘　　要：提出一类新的求解无约束优化问题的记忆梯度法,在较弱条件下证明了算法具有全局收敛性和线性收敛速率.算法采用曲线搜索方法,在每一步同时确定搜索方向和步长,收敛稳定,并且不需计算和存储矩阵,适于求解大规模优化问题.数值试验表明算法是有效的.This paper presents a new class of memory gradient method for unconstrained optimization problems.The global convergence and linear convergence rate are proved under some mild conditions.This method uses some curve search rules to determine the search direction and the step-size simultaneously at each iteration,and avoids the computation and storage of some matrices associated with the Hessian of objective functions.This makes the method converge stably and be more suitable to solve large scale optimization problems.Numerical experiments show that our algorithm is available and effective in practical computation.

关 键 词：无约束优化 记忆梯度法 曲线搜索 收敛性 

分 类 号：O221.2[理学—运筹学与控制论]