三项修正LS共轭梯度方法及其收敛性研究  

Three-term Modified Ls Conjugate Gradient Method with Its Global Convergence

作　　者：刘金魁[1] 张春涛[1] LIU JINKUI;ZHANG CHUNTAO(School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China)

机构地区：[1]重庆三峡学院数学与统计学院,万州404100

出　　处：《应用数学学报》2017年第6期862-873,共12页Acta Mathematicae Applicatae Sinica

基　　金：重庆市基础科学与前沿技术研究专项项目(cstc2017jcyjAX0318);重庆市教委科学技术研究项目(KJ1710251);重庆三峡学院重点项目(14ZD-14);重庆高校创新团队建设计划项目(CXTDX201601035);重庆市高校市级重点实验室项目(编号:[2017]3)资助

摘　　要：基于著名的LS和CG_DESCENT共轭梯度方法,本文研究了一种求解大规模无约束优化问题的非线性三项共轭梯度方法.该方法能够在每一步迭代中产生一个充分下降的搜索方向,且不依赖于任何线搜索条件.在强Wolfe线搜索条件下,新方法具有全局收敛性质·数值试验表明,新方法对给定的测试问题是有效的和稳定的.Based on the famous LS and CG_DESCENT conjugate gradient methods, a nonlinear three-term conjugate gradient method is proposed for solving large-scaled uncon- strained optimization problems. The proposed method can generate a sufficient descent direction at each iteration, which is independent of any line search. The global convergence of the proposed method is also established under the strong Wolfe line search conditions. Numerical experiments show that the proposed method is efficient and robust.

关 键 词：非线性共轭梯度方法 强Wolfe线搜索 充分下降性 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]