[1]张纯,孙文瑜,陈俊,等.一种新的非单调梯度路径线搜索方法(英文)[J].南京师大学报(自然科学版),2011,34(03):1-6.
　Zhang Chun,Sun Wenyu,Chen Jun,et al.A New Nonmonotone Gradient-Path Algorithm for Unconstrained Optimization[J].Journal of Nanjing Normal University(Natural Science Edition),2011,34(03):1-6.
点击复制

一种新的非单调梯度路径线搜索方法(英文)()
分享到：

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第34卷
期数:
2011年03期
页码:
1-6
栏目:
数学
出版日期:
2011-09-20

文章信息/Info

Title:
A New Nonmonotone Gradient-Path Algorithm for Unconstrained Optimization
作者:
张纯1; 孙文瑜2; 陈俊3; 张瑰1
( 1． 中国人民解放军理工大学理学院，江苏南京211101) ( 2． 南京师范大学数学科学学院，江苏南京210046) ( 3． 南京晓庄学院数学与信息技术学院，江苏南京211171)
Author(s):
Zhang Chun1; Sun Wenyu2; Chen Jun3; Zhang Gui1
1.Institute of Science,PLA University of Science and Technology,Nanjing 211101,China
关键词:
无约束优化; 梯度路径; 非单调技术; 全局收敛性
Keywords:
unconstrained optimization; gradient-path; nonmonotone technique; global convergence
分类号:
O224
摘要:
通过近似处理割线方程提出一种解无约束优化问题的单调梯度路径算法.其中,非单调技术用于加速目标函数的收敛过程.理论分析给出了算法的弱全局收敛性,数值结果表明了算法的有效性.
Abstract:
This paper presents a nonmonotone gradient-path algorithm by approximating the secant equation for unconstrained optimization problem． The nonmonotone criterion is used to speed up the convergence progress of objective function． Theoretical analysis is given which proves that the proposed algorithm is weakly globally convergent． The results of numerical experiments are reported to show the effectiveness of the proposed algorithm．

参考文献/References:

［1］ Botsaris C A，Jacobson D H． A Newton-type curvilinear search method for optimization［J］． Journal of Mathematical Analysis and Applications，1976， 54( 1) : 217-229．
［2］ Barzilai J，Borwein J M． Two-point step size gradient method［J］． IMA Journal of Numerical Analysis，1988，8 ( 1) : 141- 148．
［3］ Grippo L，Lampariello F，Lucidi S． A nonmonotone line search technique for Newton method［J］． SIAM Journal on Numerical Analysis，1986， 23( 4) : 707-716．
［4］ Sun W． Nonmonotone optimization methods: motivation and development［C］/ / 4th International Conference on Numerical Linear Algebra and Optimization． Guilin，2003．
［5］ Sun W． Nonmonotone trust region method for solving optimization problems［J］． Applied Mathematics and Computation， 2004，156( 1) : 159-174．
［6］ Sun W，Yuan Y． Optimization Theory and Methods: Nonlinear Programming［M］． New York: Springer，2006．
［7］ Sun W，Zhou Q． An unconstrained optimization method using nonmonotone second order Goldstein’s line search［J］． Science in China Series A: Mathematics，2007，50( 10) : 1 389-1 400．
［8］ Yang Y，Sun W． Adaptive conic trust-region method for nonlinear least squares problems［J］． Journal of Nanjing Normal University， 2007，30( 1) : 13-21．
［9］ Zhang Y，Sun W，Qi L． A Nonmonotone filter Barzilai-Borwein method for optimization［J］． Asia Pacific Journal of Operational Research，2010，27( 1) : 55-69．
［10］ Zhu D T． A family improved secant methods via nonmonotone curvilinear paths technique for equality constrained optimization ［J］． Journal of Computational and Applied Mathematics，2001，136( 1 /2) : 73-97．
［11］ Raydan M． The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem［J］． SIAM J OPTIM，1997，7 ( 1) : 26-33．

备注/Memo

备注/Memo:
Foundation item: Supported by the National Natural Science Foundation of China( 10871098，1 1071122) ， the Special Research Foundation of Doctoral Program of Higher Education of China( 20103207110002) ， the Advanced Roserch Foundation of PLA University of Science and Technology ( 20110516) ．
Corresponding author: Sun Wenyu，professor，majored in numerical mathematics． E-mail: wysun@ njnu． edu． cn
更新日期/Last Update: 2011-09-15