[1]杨 扬,孙文瑜.求解非线性最小二乘问题的自适应锥模型信赖域算法(英文)[J].南京师大学报(自然科学版),2007,30(01):13-21.
　Yang Yang,Sun Wenyu.Adaptive Conic Trust-Region Method for Nonlinear Least Squares Problems[J].Journal of Nanjing Normal University(Natural Science Edition),2007,30(01):13-21.
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求解非线性最小二乘问题的自适应锥模型信赖域算法(英文)()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第30卷
期数:
2007年01期
页码:
13-21
栏目:
数学
出版日期:
2007-03-30

文章信息/Info

Title:
Adaptive Conic Trust-Region Method for Nonlinear Least Squares Problems
作者:
杨  扬1;  孙文瑜2
( 1. 徐州工程学院数学与物理科学学院, 江苏徐州221008 )
( 2. 南京师范大学数学与计算机科学学院, 江苏南京210097 )
Author(s):
Yang Yang1; Sun Wenyu2
1.School of Mathematics and Physics Science,Xuzhou Institute of Technology,Xuzhou 221008,China
2. School ofMathem atics and Com puter S cien ce, Nan jing Norm alUn iversity, Nan jing 210097, Ch ina
关键词:
非线性最小二乘问题;  信赖域方法;  锥模型;  自适应;  总体收敛性;  超线性收敛性
Keywords:
non l inear least squares p rob lem s;  trus t reg ion m ethod;  con icm ode; l global convergen ce;  superlinear convergence
分类号:
O221.2
摘要:
针对非线性最小二乘问题,利用锥模型算法思想,给出了海赛矩阵中二阶信息项的割线近似的不同校正公式,并利用自适应信赖域技术给出了求解非线性最小二乘问题的自适应锥模型信赖域算法.算法中我们允许使用非精确方法近似求解信赖域子问题.文中给出了新算法的全局收敛性和超线性收敛性分析以及数值试验结果.
Abstract:
In th is p aper, a n ew m ethod for non l inear least-squares p rob lem s is presented. Th e m ethod uses the quas-i N ew ton update of the Gau ss-New tonH ess ian based on a con icm ode.l A m ethod w ith adapt ive tru st region strategy is cons tructed. Th em eth od n eed s to solve th e tru st reg ion subprob lem w ith a con ic m ode,l wh ich can be tran sform ed to the trust region subproblem w ith a quad ratic mode.l So the algorithm is easily imp lem en ted. The new algorithm is an alyzed and its glob al and local sup erlin ear convergence resu lts is estab lished. Num erical tes ts are presen ted that con firm the eff-i ciency of the new algorithm.

参考文献/References:

[ 1]  Denn is J E, Gay D M, W elsch R E. An adaptive non linear least-squares algorithm [ J]. ACM Transac tions onM a th Softw are, 1981( 7): 348-368.
[ 2]  Denn is J E, Gay D M, W elsch R E. Algor ithm s 573 NL2SOL- an adaptive non linear least a lgo rithm E4[ J]. ACM T ransactions on M ath Softw are, 1981( 7): 369-383.
[ 3]  Dav idonW C. Con ic approx im ation and co llinear sca ling fo r optim izers[ J]. SIAM J Num er Ana, 1980( 17) : 268-281.
[ 4]  H an Q M, Sheng S B. Con icm ode l algorithm s for non linear least-squares prob lem s[ J]. Nume ricalM athem atics, A Journal o f Ch ineseUn ive rs ities, 1995( 1): 48-59.
[ 5]  Yuan Y, SunW. Optim ization Theory andM e thods[M ] . B eijing: Sc ience Press, 1997.
[ 6]  Zhang X S, Zhang J L, L iao L Z, et a.l An adaptive trust reg ion me thod and its converg ence[ J]. Sc ience in Ch ina ( SeriesA ), 2002, 45: 620-631.
[ 7]  Schnabel R B, Eskow E. A new m od ified cho lesky factoriza tion[ J]. SIAM Journa l on Scien tific Com puting, 1990( 11):1 136-1 158.
[ 8]  Moré J J, Garbow B S, H illstrom K E. Testing unconstra ined optim ization so ftw are[ J]. ACM T ransM ath So ftw are, 1981,7( 1): 17-41.
[ 9]  S teihaug T. The con jug ate g radien tm ethod and trust reg ion in la rge sca le optim iza tion[ J] . S IAM J Nume rAna,l 1983( 20):
626-637.

相似文献/References:

[1]后六生,孙文瑜.三项预处理共轭梯度法与信赖域子问题[J].南京师大学报(自然科学版),2001,24(03):1.
　Hou Liusheng,Sun Wenyu.Three-Term Preconditioned Conjugate Gradient Method and Trust Region Subproblem[J].Journal of Nanjing Normal University(Natural Science Edition),2001,24(01):1.

备注/Memo

备注/Memo:
Foundation item: Supported by the N at iona lNatu ral Science Foundation of Ch in a ( 10231060 ), the SpecialResearch Found of DoctoralProgram of Higher Education of C h ina( 20040319003) , the Research Project of Xuzhou Inst itu te ofTechnology(XKY200622) .
Biography: Yang Y ang, born in 1981, fema le, teach ing assistant, m ajored in num ericalm ath emat ics. E-m ail:yangyoung600@ sina. com.
Corresponding autho r: SunW enyu, born in 1949, p rofessor, m ajored in num ericalm athem at ics. E-m ail:wysun@ n jnu. edu. cn
更新日期/Last Update: 2013-05-05