Levenberg–Marquardt method for solving systems of absolute value equations

Abstract

In this paper, we suggest and analyze the Levenberg-Marquardt method for solving system of absolute value equationsx R ∈ is unknown. We present different line search methods to convey the main idea and the significant modifications. We discuss the convergence of the proposed method.We consider numerical examples to illustrate the implementation and efficiency of the method. Results are very encouraging and may stimulate further research in this direction. MSC: 65K10, 65H10

On the global convergence of the inexact semi-smooth Newton method for absolute value equation

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“…As we all know, the implicit fixed-point equation which is equivalent to the LCP(q, M ) is a absolute value equation. Iqbel et al [14] proposed Levenberg-Marquardt method for solving absolute value equations, which is the combination of steepest descent and the Gauss-Newton methods. They proved the global convergence of new method when using the Goldstein line search.…”