一类充分下降的谱共轭梯度法  

A Sufficient Descent Spectral Conjugate Gradient Method

作　　者：陈龙卫[1,2] 夏福全[3] 贾朝勇[3] 

机构地区：[1]南京航空航天大学理学院,南京210016 [2]泰州机电高等职业技术学校自动化系,江苏泰州225300 [3]蚌埠学院数理系,安徽蚌埠233030

出　　处：《重庆师范大学学报（自然科学版）》2013年第4期10-14,共5页Journal of Chongqing Normal University:Natural Science

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.

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 

分 类 号：O224[理学—运筹学与控制论]