Nonmonotone Levenberg-Marquardt algorithms and their convergence analysis

J. Z. Zhang; L. H. Chen

doi:10.1023/A:1022615415582

Nonmonotone Levenberg-Marquardt algorithms and their convergence analysis

J. Z. Zhang
, L. H. Chen

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

23 Citations (Scopus)

Abstract

In this paper, two nonmonotone Levenberg-Marquardt algorithms for unconstrained nonlinear least-square problems with zero or small residual are presented. These algorithms allow the sequence of objective function values to be nonmonotone, which accelerates the iteration progress, especially in the case where the objective function is ill-conditioned. Some global convergence properties of the proposed algorithms are proved under mild conditions which exclude the requirement for the positive definiteness of the approximate Hessian T(x). Some stronger global convergence properties and the local superlinear convergence of the first algorithm are also proved. Finally, a set of numerical results is reported which shows that the proposed algorithms are promising and superior to the monotone Levenberg-Marquardt algorithm according to the numbers of gradient and function evaluations.
© 1997 Plenum Publishing Corporation

Original language	English
Pages (from-to)	393-418
Journal	Journal of Optimization Theory and Applications
Volume	92
Issue number	2
DOIs	https://doi.org/10.1023/A:1022615415582
Publication status	Published - Feb 1997
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

This research was partially supported by City University of Hong Kong Grant 7000308.

Research Keywords

Levenberg-Marquardt algorithm
Nonlinear least-square problems
Nonmonotone techniques

Access Output

10.1023/A:1022615415582

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{12419e8731bd4879b734c1055484946a,

title = "Nonmonotone Levenberg-Marquardt algorithms and their convergence analysis",

abstract = "In this paper, two nonmonotone Levenberg-Marquardt algorithms for unconstrained nonlinear least-square problems with zero or small residual are presented. These algorithms allow the sequence of objective function values to be nonmonotone, which accelerates the iteration progress, especially in the case where the objective function is ill-conditioned. Some global convergence properties of the proposed algorithms are proved under mild conditions which exclude the requirement for the positive definiteness of the approximate Hessian T(x). Some stronger global convergence properties and the local superlinear convergence of the first algorithm are also proved. Finally, a set of numerical results is reported which shows that the proposed algorithms are promising and superior to the monotone Levenberg-Marquardt algorithm according to the numbers of gradient and function evaluations. {\textcopyright} 1997 Plenum Publishing Corporation",

keywords = "Levenberg-Marquardt algorithm, Nonlinear least-square problems, Nonmonotone techniques",

author = "Zhang, \{J. Z.\} and Chen, \{L. H.\}",

note = "Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].",

year = "1997",

month = feb,

doi = "10.1023/A:1022615415582",

language = "English",

volume = "92",

pages = "393--418",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Nonmonotone Levenberg-Marquardt algorithms and their convergence analysis

AU - Zhang, J. Z.

AU - Chen, L. H.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 1997/2

Y1 - 1997/2

N2 - In this paper, two nonmonotone Levenberg-Marquardt algorithms for unconstrained nonlinear least-square problems with zero or small residual are presented. These algorithms allow the sequence of objective function values to be nonmonotone, which accelerates the iteration progress, especially in the case where the objective function is ill-conditioned. Some global convergence properties of the proposed algorithms are proved under mild conditions which exclude the requirement for the positive definiteness of the approximate Hessian T(x). Some stronger global convergence properties and the local superlinear convergence of the first algorithm are also proved. Finally, a set of numerical results is reported which shows that the proposed algorithms are promising and superior to the monotone Levenberg-Marquardt algorithm according to the numbers of gradient and function evaluations. © 1997 Plenum Publishing Corporation

AB - In this paper, two nonmonotone Levenberg-Marquardt algorithms for unconstrained nonlinear least-square problems with zero or small residual are presented. These algorithms allow the sequence of objective function values to be nonmonotone, which accelerates the iteration progress, especially in the case where the objective function is ill-conditioned. Some global convergence properties of the proposed algorithms are proved under mild conditions which exclude the requirement for the positive definiteness of the approximate Hessian T(x). Some stronger global convergence properties and the local superlinear convergence of the first algorithm are also proved. Finally, a set of numerical results is reported which shows that the proposed algorithms are promising and superior to the monotone Levenberg-Marquardt algorithm according to the numbers of gradient and function evaluations. © 1997 Plenum Publishing Corporation

KW - Levenberg-Marquardt algorithm

KW - Nonlinear least-square problems

KW - Nonmonotone techniques

UR - https://www.scopus.com/pages/publications/0031504169

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0031504169&origin=recordpage

U2 - 10.1023/A:1022615415582

DO - 10.1023/A:1022615415582

M3 - RGC 21 - Publication in refereed journal

SN - 0022-3239

VL - 92

SP - 393

EP - 418

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 2

ER -

Nonmonotone Levenberg-Marquardt algorithms and their convergence analysis

Abstract

Bibliographical note

Funding

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Cite this