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<p>In this paper, an inertial-based hybrid three-term conjugate gradient projection (CGP) algorithm is proposed for solving constrained nonlinear equations. This algorithm exhibits several key theoretical features: (1) A hybrid three-term search direction is constructed using the hybrid technique, ensuring both sufficient descent and trust region properties. (2) An inertial extrapolation step is incorporated into the algorithm, enhancing its efficiency. (3) The global convergence of the algorithm is rigorously analyzed, without relying on the Lipschitz continuity of the nonlinear equations. (4) Preliminary numerical experiments on standard constrained nonlinear equations and image denoising problems are reported, which demonstrate the effectiveness and superiority of the proposed algorithm when compared to existing methods.</p>

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Solving constrained nonlinear equations with an inertial-based hybrid three-term CGP algorithm: application to image denoising

  • 期刊论文

  • 发表日期：

    2025年5月20日

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  • Dandan Li,
  • Yong Li,
  • Songhua Wang

摘要

In this paper, an inertial-based hybrid three-term conjugate gradient projection (CGP) algorithm is proposed for solving constrained nonlinear equations. This algorithm exhibits several key theoretical features: (1) A hybrid three-term search direction is constructed using the hybrid technique, ensuring both sufficient descent and trust region properties. (2) An inertial extrapolation step is incorporated into the algorithm, enhancing its efficiency. (3) The global convergence of the algorithm is rigorously analyzed, without relying on the Lipschitz continuity of the nonlinear equations. (4) Preliminary numerical experiments on standard constrained nonlinear equations and image denoising problems are reported, which demonstrate the effectiveness and superiority of the proposed algorithm when compared to existing methods.