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<p>The goal of this paper is to establish the projection-based iterative algorithm for solving a large-scale system of monotone nonlinear equations. The algorithm we propose here is the three-term derivative-free method, which generates a search direction guaranteeing sufficient descent and trust region properties regardless of the line search technique employed. It is shown that the algorithm is globally convergent without requiring Lipschitz continuity assumptions on the objective function. The performed numerical results demonstrate the feasibility and efficiency of the proposed algorithm.</p>

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An efficient spectral three-term derivative-free projection algorithm for a large-scale system of monotone nonlinear equations

  • 期刊论文

  • 发表日期：

    2025年2月5日

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  • Qun Li,
  • Guolin Chen,
  • Maolin Liang

摘要

The goal of this paper is to establish the projection-based iterative algorithm for solving a large-scale system of monotone nonlinear equations. The algorithm we propose here is the three-term derivative-free method, which generates a search direction guaranteeing sufficient descent and trust region properties regardless of the line search technique employed. It is shown that the algorithm is globally convergent without requiring Lipschitz continuity assumptions on the objective function. The performed numerical results demonstrate the feasibility and efficiency of the proposed algorithm.