一类新的记忆梯度法及其全局收敛性  

A new class of memory gradient methods and its global convergence

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：《纯粹数学与应用数学》2010年第2期251-256,共6页Pure and Applied Mathematics

基　　金：国家自然科学基金(10571109);信阳师范学院青年科研基金(200946;200947)

摘　　要：研究了求解无约束优化问题的记忆梯度法,利用当前和前面迭代点的信息产生下降方向,得到了一类新的无约束优化算法,在Wolfe线性搜索下证明了其全局收敛性.新算法结构简单,不用计算和存储矩阵,适于求解大型优化问题.数值试验表明算法有效.In this paper,the memory gradient method for unconstrained optimization problems is concerned.A new unconstrained optimization algorithm is presented by using the current and previous iterative information to generate a decent direction.We prove the global convergence under the Wolfe line search.The method has a simple structure and avoids the computation and storage of some matrices.It is suitable to solve large scale optimization problems.Numerical experiment shows that the new algorithm is not only feasible but also effective.

关 键 词：无约束优化 记忆梯度法 Wolfe线性搜索 全局收敛 

分 类 号：O221.2[理学—运筹学与控制论]