A MODIFIED LEVENBERG-MARQUARDT METHOD WITH A NON-MONOTONE LINE SEARCH FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

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AMINI K.; ROSTAMI F.

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Journal Paper

Paper Information

Journal: Journal of Operational Research in its Applications Year:2016 | Volume:12 | Issue:4 (47) Page(s): 1-14

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Title

A MODIFIED LEVENBERG-MARQUARDT METHOD WITH A NON-MONOTONE LINE SEARCH FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

Author(s)

AMINI K. | ROSTAMI F. | Issue Writer Certificate

Keywords

NON-LINEAR SYSTEM OF EQUATIONS

LEVENBERG- MARQUARDT METHOD

LOCAL BOUNDARY CONDITION ERROR

NON-UNIFORM LINEAR SEARCH

Abstract

In this paper, we propose a new modified Levenberg–Marquardt algorithm for solving systems of nonlinear equations while the trail step, at any iteration, is set as the sum of the general LM step with a corrected LM direction. The new method also uses a modified non-monotone line search rule when the modified direction can’t generate an appropriate reduction. Under the local error bound condition, we show the local cubic convergence of the algorithm. Some numerical experiments are given to illustrate the performance and efficiency of the presented algorithm.

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References

NEWTON-LIKE ITERATIVE METHODS FOR SOLVING THE SYSTEMS OF NONLINEAR EQUATIONS

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APA: Copy

AMINI, K., & ROSTAMI, F.. (2016). A MODIFIED LEVENBERG-MARQUARDT METHOD WITH A NON-MONOTONE LINE SEARCH FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), 12(4 (47)), 1-14. SID. https://sid.ir/paper/164448/en

Vancouver: Copy

AMINI K., ROSTAMI F.. A MODIFIED LEVENBERG-MARQUARDT METHOD WITH A NON-MONOTONE LINE SEARCH FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS)[Internet]. 2016;12(4 (47)):1-14. Available from: https://sid.ir/paper/164448/en

IEEE: Copy

K. AMINI, and F. ROSTAMI, “A MODIFIED LEVENBERG-MARQUARDT METHOD WITH A NON-MONOTONE LINE SEARCH FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS,” JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), vol. 12, no. 4 (47), pp. 1–14, 2016, [Online]. Available: https://sid.ir/paper/164448/en

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