On convergence of a truncated Gauss-Newton method for solving underdetermined nonlinear least squares problems

Ji Feng Bao; Sy Ming Guu; Jinhua Wang; Yaohua Hu; Chong Li

On convergence of a truncated Gauss-Newton method for solving underdetermined nonlinear least squares problems

Ji Feng Bao^*
, Sy Ming Guu
, Jinhua Wang
, Yaohua Hu
, Chong Li

^*Corresponding author for this work

Graduate Institute of Mangement

Zhejiang Ocean University
Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province
Zhejiang University of Technology
Shenzhen University
Zhejiang University

Research output: Contribution to journal › Journal Article › peer-review

Abstract

We consider a truncated Gauss-Newton method for solving nonlinear least squares problems (NLSP) for the underdetermined case. Under some mild conditions, the method converges to a solution at rate of ν when the involved parameter ν in the truncated method satisfies ν ∈ (1,2], and superlinearly when ν = 1 and θ_k → 0. It should be remarked that our techniques for convergence analysis are quite different from that used in [Appl. Numer. Math., Ill, 92-110 (2017)].

Original language	English
Pages (from-to)	2235-2246
Number of pages	12
Journal	Journal of Nonlinear and Convex Analysis
Volume	19
Issue number	12
State	Published - 2018

Bibliographical note

Publisher Copyright:
© 2018.

Keywords

Inexact Levenberg-Marquardt method
Nonlinear least squares problems
Superlinear convergence
Truncated Gauss-Newton method

Cite this

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abstract = "We consider a truncated Gauss-Newton method for solving nonlinear least squares problems (NLSP) for the underdetermined case. Under some mild conditions, the method converges to a solution at rate of ν when the involved parameter ν in the truncated method satisfies ν ∈ (1,2], and superlinearly when ν = 1 and θk → 0. It should be remarked that our techniques for convergence analysis are quite different from that used in [Appl. Numer. Math., Ill, 92-110 (2017)].",

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T1 - On convergence of a truncated Gauss-Newton method for solving underdetermined nonlinear least squares problems

AU - Bao, Ji Feng

AU - Guu, Sy Ming

AU - Wang, Jinhua

AU - Hu, Yaohua

AU - Li, Chong

PY - 2018

Y1 - 2018

N2 - We consider a truncated Gauss-Newton method for solving nonlinear least squares problems (NLSP) for the underdetermined case. Under some mild conditions, the method converges to a solution at rate of ν when the involved parameter ν in the truncated method satisfies ν ∈ (1,2], and superlinearly when ν = 1 and θk → 0. It should be remarked that our techniques for convergence analysis are quite different from that used in [Appl. Numer. Math., Ill, 92-110 (2017)].

AB - We consider a truncated Gauss-Newton method for solving nonlinear least squares problems (NLSP) for the underdetermined case. Under some mild conditions, the method converges to a solution at rate of ν when the involved parameter ν in the truncated method satisfies ν ∈ (1,2], and superlinearly when ν = 1 and θk → 0. It should be remarked that our techniques for convergence analysis are quite different from that used in [Appl. Numer. Math., Ill, 92-110 (2017)].

KW - Inexact Levenberg-Marquardt method

KW - Nonlinear least squares problems

KW - Superlinear convergence

KW - Truncated Gauss-Newton method

UR - https://www.scopus.com/pages/publications/85060515717

M3 - 文章

AN - SCOPUS:85060515717

SN - 1345-4773

VL - 19

SP - 2235

EP - 2246

JO - Journal of Nonlinear and Convex Analysis

JF - Journal of Nonlinear and Convex Analysis

IS - 12

ER -

On convergence of a truncated Gauss-Newton method for solving underdetermined nonlinear least squares problems

Abstract

Bibliographical note

Keywords

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