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<p>In this paper, we reformulate the horizontal linear complementarity problem as a system of smooth nonlinear equations using a smoothing technique. We then propose a modulus-based smoothing Levenberg–Marquardt method to solve this system. By introducing the trust region technique, we establish the global convergence of the proposed method. Furthermore, under the local error bound condition, we prove its quadratic convergence. Numerical results are reported to show the efficiency of the proposed method.</p>

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The modulus-based smoothing Levenberg–Marquardt method for solving horizontal linear complementarity problems

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Si-Wei Liao,
  • Guo-Feng Zhang,
  • Zhao-Zheng Liang

摘要

In this paper, we reformulate the horizontal linear complementarity problem as a system of smooth nonlinear equations using a smoothing technique. We then propose a modulus-based smoothing Levenberg–Marquardt method to solve this system. By introducing the trust region technique, we establish the global convergence of the proposed method. Furthermore, under the local error bound condition, we prove its quadratic convergence. Numerical results are reported to show the efficiency of the proposed method.