摘要
基于经典PRP(Polak-Ribière-Polyak)算法,设计一个具有充分下降性和信赖域性质的搜索方向,采用投影技术及经典单调线搜索,提出一种求解大规模非线性单调方程组的修正共轭梯度算法.在常规条件下,新算法具有全局收敛性.初步的数值实验结果表明:新算法比经典PRP算法和3项PRP算法效率更优,鲁棒性更好,适合求解大规模非线性单调方程组.
Based on the classical PRP method,a search direction,which has a sufficient descent feature and a trust region trait,was designed.For large scale nonlinear monotone equations,a modified conjugate method was proposed under the projection technique and classical monotone line search.In some reasonable conditions,the proposed algorithm possessed the global convergence property.Numerical results proved that the new algorithm was perfect and had good robustness in comparison with classical PRP method and three-terms PRP method.Therefore,it was better to solve large scale nonlinear monotone equations.
作者
王松华
罗丹
黎勇
WANG Songhua;LUO Dan;LI Yong(College of Mathematics and Statistics Science,Baise University,Baise 533000,China)
出处
《安徽大学学报（自然科学版）》
CAS
北大核心
2023年第5期15-21,共7页
Journal of Anhui University(Natural Science Edition)
基金
国家自然科学基金资助项目(11661009)
广西自然科学基金资助项目(2020GXNSFAA159069)
中央引导地方科技发展专项资金资助(桂科ZY20198003)。
关键词
非线性单调方程组
共轭梯度法
投影技术
全局收敛性
nonlinear monotone equations
conjugate gradient
projection technique
global convergence
