Paper Information

Journal:   JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS)   WINTER 2016 , Volume 12 , Number 4 (47); Page(s) 1 To 14.
 
Paper: 

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

 
 
Author(s):  AMINI K.*, ROSTAMI F.
 
* DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, RAZI UNIVERSITY, KERMANSHAH, IRAN
 
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.

 
Keyword(s): NON-LINEAR SYSTEM OF EQUATIONS, LEVENBERG- MARQUARDT METHOD, LOCAL BOUNDARY CONDITION ERROR, NON-UNIFORM LINEAR SEARCH
 
References: 
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