Modified inexact Levenberg–Marquardt methods for solving nonlinear least squares problems

Jifeng Bao (), Carisa Kwok Wai Yu (), Jinhua Wang (), Yaohua Hu () and Jen-Chih Yao ()
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Jifeng Bao: Zhejiang Ocean University
Carisa Kwok Wai Yu: The Hang Seng University of Hong Kong
Jinhua Wang: Zhejiang University of Technology
Yaohua Hu: Shenzhen University
Jen-Chih Yao: China Medical University

Computational Optimization and Applications, 2019, vol. 74, issue 2, No 7, 547-582

Abstract: Abstract 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.

Keywords: Nonlinear least squares problems; Inexact Levenberg–Marquardt method; Lipschitz condition; Local error bound; 65K05; 93E24 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-019-00111-y

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