Modified inexact Levenberg–Marquardt methods for solving nonlinear least squares problems
Modified inexact Levenberg–Marquardt methods for solving nonlinear least squares problems
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DOI：
10.1007/s10589-019-00111-y
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发表时间：
2019-05
影响因子：
2.2
通讯作者：
Jifeng Bao;C. Yu;Jinhua Wang;Yaohua Hu;J. Yao
中科院分区：
文献类型：
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作者：
Jifeng Bao;C. Yu;Jinhua Wang;Yaohua Hu;J. Yao
本文利用Armijo、Wolfe或Goldstein线搜索格式，提出了求解非线性最小二乘问题(NLSP)的一种改进的不精确Levenberg-MarQuardt方法(LMM)及其全局形式，特别是在欠定情况下。在局部误差界条件下，证明了修正的非精确LMM生成的序列对某些特殊参数具有超线性甚至二次收敛的性质，改进了Dan等人的相应结果。(OpTim方法软件17：605-626,2002)。此外，还证明了修正的非精确LMM的全局形式的二次收敛。最后，对一些中、大规模的欠定NLSP问题进行了初步的数值实验，结果表明我们的算法比经典的非精确LMM算法有更好的性能。
In the present paper, we propose a modified inexact Levenberg–Marquardt method (LMM) and its global version by virtue of Armijo, Wolfe or Goldstein line-search schemes to solve nonlinear least squares problems (NLSP), especially for the underdetermined case. Under a local error bound condition, we show that a sequence generated by the modified inexact LMM converges to a solution superlinearly and even quadratically for some special parameters, which improves the corresponding results of the classical inexact LMM in Dan et al. (Optim Methods Softw 17:605–626, 2002). Furthermore, the quadratical convergence of the global version of the modified inexact LMM is also established. Finally, preliminary numerical experiments on some medium/large scale underdetermined NLSP show that our proposed algorithm outperforms the classical inexact LMM.