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<p>In this paper we study an inexact version of the modified Levenberg-Marquardt method for solving nonlinear equations. The proposed approach computes both the Levenberg-Marquardt step and its approximation inexactly at every iteration. Under the local error bound condition, we derive the convergence order of this inexact method without line search. Furthermore, we develop an inexact modified Levenberg-Marquardt method incorporating line search strategy, and prove its global convergence as well as local fast convergence rate. Numerical experiments demonstrate that the proposed inexact modified Levenberg-Marquardt method outperforms several existing Levenberg-Marquardt type methods.</p>

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Analysis of the inexact modified Levenberg-Marquardt method for nonlinear equations

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Jingyong Tang,
  • Yulong Ma

摘要

In this paper we study an inexact version of the modified Levenberg-Marquardt method for solving nonlinear equations. The proposed approach computes both the Levenberg-Marquardt step and its approximation inexactly at every iteration. Under the local error bound condition, we derive the convergence order of this inexact method without line search. Furthermore, we develop an inexact modified Levenberg-Marquardt method incorporating line search strategy, and prove its global convergence as well as local fast convergence rate. Numerical experiments demonstrate that the proposed inexact modified Levenberg-Marquardt method outperforms several existing Levenberg-Marquardt type methods.