摘要
谱共轭梯度算法是求解大规模无约束最优化问题的有效算法之一.基于Hestenes-Stiefel算法与谱共轭梯度算法,提出一种谱Hestenes-Stiefel共轭梯度算法.在Wolfe线搜索下,算法产生的搜索方向具有下降性质,且全局收敛性也能得到证明.通过对CUTEr函数库中部分著名的函数进行试验,利用著名的Dolan&More评价体系,展示了新算法的有效性.
The spectral conjugate gradient method is one successful method to solve largescale unconstrained optimization problems.In this paper,a spectral Hestenes-Stiefel conjugate gradient method is proposed based on the HS＋ method and the spectral gradient method.The proposed method generates the decent search direction at each iterate under the Wolfe line searches.Under some mild conditions,the global convergence of the proposed method is proved.By the famous evaluation method of Dolan More,preliminary numerical results also show that the proposed methods are stable and efficient for some given large-scale unconstrained optimization problems.
出处
《数学的实践与认识》
北大核心
2015年第18期261-270,共10页
Mathematics in Practice and Theory
关键词
无约束最优化
共轭梯度算法
谱梯度算法
WOLFE线搜索
全局收敛性
unconstrained optimization
conjugate gradient method
spectral gradient method
wolfeline search
global convergence
