Wolfe线搜索下两种修正DY共轭梯度法的全局收敛性  

The Global Convergence of Modified DY Conjugate Gradient Methods under the Wolfe Line Search

作　　者：周雪琴[1] 卢琳璋[1] 

机构地区：[1]贵州师范大学数学与计算机科学学院,贵阳550001

出　　处：《重庆师范大学学报（自然科学版）》2016年第3期6-10,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11261012)

摘　　要：提出了两个修正的DY(Dai-Yuan)共轭梯度法(ZDY1算法和ZDY2算法),并证明这两个修正的共轭梯度法公式β_k^((1))和β_k^((2))在Wolfe下都是全局收敛的,其中一个在Wolfe线搜索下是下降的,另一个在不依赖于任何线搜索下充分下降。在求解大规模的非线性优化问题的过程中,这些结果对加快算法的收敛速度和增强算法的收敛性提供了理论依据。Two modified DY conjugate gradient methods（Algorithm ZDY1 and Algorithm ZDY2）based on the Dai-Yuan method are proposed for unconstrained optimization problems.We prove the global convergence of the two modified DY conjugate gradient methods under the standard Wolfe line search.One of the two modified methods provides a descent direction with the Wolfe line search,the other keeps a sufficient descent direction without any line search.In the process of solving large-scale nonlinear optimization problems,these results provide theory bases to accelerate the convergence speed and enhance the convergence of the algorithm.

关 键 词：共轭梯度法 下降性 充分下降性 WOLFE线搜索 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]