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

Autor:	Jen-Chih Yao, Jifeng Bao, Carisa Kwok Wai Yu, Jinhua Wang, Yaohua Hu
Rok vydání:	2019
Předmět:	Quadratic growth Sequence 021103 operations research Control and Optimization Underdetermined system Scale (ratio) Applied Mathematics 0211 other engineering and technologies 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Levenberg–Marquardt algorithm Computational Mathematics Non-linear least squares Convergence (routing) Applied mathematics 0101 mathematics Mathematics
Zdroj:	Computational Optimization and Applications. 74:547-582
ISSN:	1573-2894 0926-6003
DOI:	10.1007/s10589-019-00111-y
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::906a8c7a8de236b7037c716b9062e240 https://doi.org/10.1007/s10589-019-00111-y Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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