求解非线性方程组的修正Fletcher-Reeves共轭梯度法  

A Modified Fletcher-Reeves Conjugate Gradient Method for Nonlinear Equations

作　　者：黎勇 罗丹 王松华 LI Yong;LUO Dan;WANG Songhua(School of Mathematics and Statistics,Baise University,Baise 533000,China)

机构地区：[1]百色学院数学与统计学院,广西百色533000

出　　处：《应用数学》2023年第3期703-710,共8页Mathematica Applicata

基　　金：国家自然科学基金(11661009);广西自然科学基金(2020GXNSFAA159069);中央引导地方科技发展专项资金(桂科ZY20198003)。

摘　　要：针对非线性方程组求解问题,本文在经典的Fletcher-Reeves(FR)共轭梯度法的基础上提出一个新的搜索方向公式,结合超平面投影技术和线搜索技术设计一种修正的FR算法.该算法不依赖任何线搜索满足充分下降条件,搜索方向具有信赖域性质,在常规假设条件下全局收敛.初步的数值实验表明,对选定的测试问题,修正的FR算法比经典FR算法更有效.On the basis of the classical FR conjugate gradient method,a new search direction is devised.Combining with the projection technique and the line search approach,A modified Fletcher-Reeves(FR) conjugate gradient algorithm for nonlinear equations is proposed.The new algorithm possesses the sufficient descent property without any line search and the proposed search direction satisfies the trust region feature.The global convergence of the proposed algorithm is established under some reasonable consumptions.The preliminary numerical experiments are reported to show that the new algorithm is more efficient than the classical FR method for some benchmark problems.

关 键 词：非线性方程组 共轭梯度法 充分下降条件 信赖域性质 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]