一个基于定步长技术的超记忆梯度法  

A Supermemory Gradient Method without Line Search

作　　者：刘元文[1] 欧宜贵[1] 马巍[1] 

机构地区：[1]海南大学信息学院数学系,海南海口570228

出　　处：《应用数学》2015年第1期74-82,共9页Mathematica Applicata

基　　金：国家自然科学基金(11261015);海南省自然科学基金(111001)

摘　　要：基于定步长技术,本文给出一种求解无约束优化问题的超记忆梯度算法,从而避免每步都执行线搜索.在一定条件下证明该算法具有全局收敛性和局部线性收敛率.由于该方法不用计算和存储矩阵,故适合于求解大规模优化问题.数值试验表明该算法是有效的.Based on a fixed step-length technique,this paper presents a new supermemory gradient method for unconstrained optimization problems, which avoids the line search at each iteration. Under some conditions,the global convergence and locally superlinear conver- gence rate are analyzed. The proposed method avoids the computation and storage of some matrices, and is suitable to solve large scale optimization problems. Preliminary numerical re- sults indicate that this algorithm is effective.

关 键 词：无约束优化 定步长技术 超记忆梯度法 数值试验 

分 类 号：O221[理学—运筹学与控制论]