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)-《南京师大学报（自然科学版）》

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

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.