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<p>This paper proposes an iterative scheme for solving constrained nonlinear monotone equations. The method was inspired by one of the open problems propounded by Andrei (Bull Malays Math Sci Soc (2) 34(2):319–330, 2011), which involves finding an optimal approximation for the parameter <i>t</i> of the classical method designed by Dai and Liao (Appl Math Optim 43(1): 87–101, 2001). Based on singular value analysis and spectral condition number of the iteration matrix of a four-term Dai–Liao scheme, a reasonable choice for <i>t</i> is obtained which ensures that the required condition for global convergence is satisfied. The proposed scheme is suitable for non-smooth problems since its implementation does not require computing derivatives. Moreover, the scheme converges globally and its effectiveness is shown by some numerical experiments and image de-blurring application.</p>

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Descent Four-Term Dai–Liao-Type Scheme for Constrained Monotone Equations and Image De-Blurring

  • 期刊论文

  • 发表日期：

    2025年10月8日

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  • Kabiru Ahmed,
  • Mohammed Yusuf Waziri,
  • Abubakar Sani Halilu,
  • Salisu Murtala

摘要

This paper proposes an iterative scheme for solving constrained nonlinear monotone equations. The method was inspired by one of the open problems propounded by Andrei (Bull Malays Math Sci Soc (2) 34(2):319–330, 2011), which involves finding an optimal approximation for the parameter t of the classical method designed by Dai and Liao (Appl Math Optim 43(1): 87–101, 2001). Based on singular value analysis and spectral condition number of the iteration matrix of a four-term Dai–Liao scheme, a reasonable choice for t is obtained which ensures that the required condition for global convergence is satisfied. The proposed scheme is suitable for non-smooth problems since its implementation does not require computing derivatives. Moreover, the scheme converges globally and its effectiveness is shown by some numerical experiments and image de-blurring application.