一种无需线搜索的共轭梯度算法及其收敛性  

A Conjugate Gradient Method Without Line Search Techniques and Its Convergence Analysis

作　　者：汪淑兰 黄贤通[1] 黄进红[1] 周根娇[2] 

机构地区：[1]赣南师范学院数学与计算机科学学院,江西赣州341000 [2]赣南师范学院科技学院,江西赣州341000

出　　处：《赣南师范学院学报》2014年第6期11-14,共4页Journal of Gannan Teachers' College(Social Science(2))

基　　金：江西省高校教改课题(JXJG-13-39-6)

摘　　要：针对无约束优化问题,结合固定步长公式和具有充分下降性质的共轭梯度算法,提出一类简单、实用,且无需任何线搜索技术的求解方法.该算法不涉及矩阵运算,特别适合大规模优化问题.并讨论该算法的全局收敛性,在一阶导数趋于零的意义下得到强收敛结果.初步的数值实验表明,该算法是有效和可行的.A simple and efficient conjugate gradient method with a sufficient descent direction and a fixed step formula is proposed in this paper. The method needs not any line search technique. It is especially suitable for large-scale optimization problems because it does not involve any matrix operation. The global convergence of the method is discussed,and the strong convergence results were obtained. Preliminary numerical result shows that the proposed method is efficient and feasible.

关 键 词：无约束优化 共轭梯度法 充分下降方向 固定步长公式 

分 类 号：O224[理学—运筹学与控制论]