种求解非线性无约束优化问题的充分下降的共轭梯度法  

A sufficient descent conjugate gradient method for nonlinear unconstrained optimization problems

作　　者：Tsegay Giday Woldu 张海斌[1] 张鑫 张芳 Tsegay Giday Woldu;ZHANG Haibin;ZHANG Xin;ZHANG Fang(College of Applied Sciences,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《运筹学学报》2018年第3期59-68,共10页Operations Research Transactions

基　　金：国家自然科学基金(Nos.61179033,11771003)。

摘　　要：共轭梯度法是一类具有广泛应用的求解大规模无约束优化问题的方法.提出了一种新的非线性共轭梯度(CG)法,理论分析显示新算法在多种线搜索条件下具有充分下降性.进一步证明了新CG算法的全局收敛性定理.最后,进行了大量数值实验,其结果表明与传统的几类CG方法相比,新算法具有更为高效的计算性能.One of the widely used methods for solving large scale unconstrained optimization problems is the conjugate gradient method.In this paper,we propose a new nonlinear conjugate gradient method(CG),which satisfies the sufficient descent condition independent of any line search.We further establish global convergence theorem of the new CG method.Finally,a large amount of numerical experiments are carried out and reported.It shows that the proposed method has an efficient computational performance.

关 键 词：无约束优化问题 非线性共轭梯度法 充分下降性 全局收敛性 

分 类 号：O221[理学—运筹学与控制论]