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A nonmonotone adaptive Levenberg-Marquardt algorithm for solving nonlinear systems of equations

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  • Dou, Tianjiao
  • Yuan, Liuyang
  • Chi, Xiaoni

Abstract

By combining the improved nonmonotone adaptive line search technique with the improved Levenberg-Marquardt algorithm (LM algorithm), a nonmonotone adaptive LM algorithm for solving nonlinear systems of equations is presented. In the new algorithm, a novel adaptive LM parameter that integrates the gradient norm and function value is introduced. Meanwhile, in the new nonmonotonic line search rule, the nonmonotonicity of the algorithm is adaptively adjusted based on the gradient norm. Under appropriate conditions, the global convergence and local convergence of the algorithm are proven. Numerical experimental results show that the algorithm in this paper is feasible and effective.

Suggested Citation

  • Dou, Tianjiao & Yuan, Liuyang & Chi, Xiaoni, 2026. "A nonmonotone adaptive Levenberg-Marquardt algorithm for solving nonlinear systems of equations," Applied Mathematics and Computation, Elsevier, vol. 525(C).
    • Handle: RePEc:eee:apmaco:v:525:y:2026:i:c:s0096300326000974
    DOI: 10.1016/j.amc.2026.130045
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