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<p>In this paper, based on the restart procedure and the inertial acceleration technique, we propose a modified three-term conjugate gradient projection method (CGPM) for solving large-scale nonlinear equations. The search direction satisfies the sufficient descent condition and the trust region property without any line search criterion. Moreover, the proposed restart direction contains an arbitrary nonzero vector to enhance flexibility. The global convergence of the proposed algorithm is established without the Lipschitz continuity. Furthermore, under the locally Lipschitz continuity assumption, we analyze the asymptotic and non-asymptotic global convergence rates. Numerical experiments conducted on the standard nonlinear equations, as well as applications in the sparse signal restoration problems, have demonstrated the numerical efficacy of our method.</p>

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A modified three-term CGPM with a new restart procedure and convergence rate analysis for solving nonlinear equations

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Guodong Ma,
  • Yue Niu,
  • Dan Jian,
  • Hongxue Shen

摘要

In this paper, based on the restart procedure and the inertial acceleration technique, we propose a modified three-term conjugate gradient projection method (CGPM) for solving large-scale nonlinear equations. The search direction satisfies the sufficient descent condition and the trust region property without any line search criterion. Moreover, the proposed restart direction contains an arbitrary nonzero vector to enhance flexibility. The global convergence of the proposed algorithm is established without the Lipschitz continuity. Furthermore, under the locally Lipschitz continuity assumption, we analyze the asymptotic and non-asymptotic global convergence rates. Numerical experiments conducted on the standard nonlinear equations, as well as applications in the sparse signal restoration problems, have demonstrated the numerical efficacy of our method.