一类无需线性搜索的记忆梯度法  

A New Memory Gradient Method Without Line Search

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》2011年第2期249-254,共6页Mathematica Applicata

基　　金：国家自然科学基金资助项目(10571109);信阳师范学院青年基金(200946)

摘　　要：提出一类新的求解无约束优化问题的记忆梯度法,证明了算法的全局收敛性.当目标函数为一致凸函数时,对其线性收敛速率进行了分析.新算法在迭代过程中无需对步长进行线性搜索,仅需对算法中的一些参数进行预测估计,从而减少了目标函数及梯度的迭代次数,降低了算法的计算量和存储量.数值试验表明算法是有效的.In this paper,we present a new memory gradient method for unconstrained optimization and prove its global convergence. The linear convergence rate is investigated when the objective function is uniformly convex. The algorithm is not required to determine the step-size by using some search rules. It only needs to estimate some parameters at each iteration of the algorithm. By this way, the algorithm reduces the number of iterations, function evaluations and gradient evaluations so as to reduce the computation and storage of the algorithm. Numerical experiments show that the new method is efficient in paractical computation.

关 键 词：无约束优化 记忆梯度法 全局收敛性 线性收敛速率 

分 类 号：O221.2[理学—运筹学与控制论]