摘要
首先基于共轭梯度法的共轭条件和下降性,提出了一类充分下降的谱共轭梯度法。该方法将经典共轭梯度法中搜索方向由原来的只满足一个共轭条件改变为同时满足一个共轭条件和一个下降条件;然后,在Wolfe线搜索下用反证法证明了新算法的全局收敛性;最后,通过12个算例,将新算法和已有SHS算法在迭代次数和计算时间方面进行了数值比较实验,比较结果表明新算法在这两个方面都明显优越于SHS算法。算法的全局收敛性和数值结果的优越性表明,新算法是一个值得研究的方法。
First,a class of sufficiently descent spectral conjugate gradient method is put forward,which satisfies both conjugacy condition and descent condition,while the standard conjugate gradient method only meets conjugacy condition.Then,the global convergence of the new method is proved with the reduction to absurdity under the Wolfe line search.Finally,iterative times and computing time are compared between the new algorithm and the existing SHS algorithm in twelve examples.The comparison results show that the new algorithm is superior to the SHS algorithm in these two aspects.The global convergence and the numerical superiority indicate that the new algorithm is an effective algorithm which is worth studying.
出处
《重庆师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第4期10-14,共5页
Journal of Chongqing Normal University:Natural Science
关键词
无约束优化
谱共轭梯度法
充分下降条件
共轭条件
全局收敛
unconstrained optimization
spectral conjugate gradient method
sufficient descent condition
conjugate condition
global convergence
