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A projection-based derivative free DFP approach for solving system of nonlinear convex constrained monotone equations with image restoration applications

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Abstract

The nonlinear programming makes use of quasi-Newton methods, a collection of optimization approaches when traditional Newton’s method are challenging due to the calculation of the Jacobian matrix and its inverse. Since the Jacobian matrix is computationally difficult to compute and sometimes not available specifically when dealing with non-smooth monotone systems, quasi-Newton methods with superlinear convergence are preferred for solving nonlinear system of equations. This paper provides a new version of the derivative-free David–Fletcher–Powell (DFP) approach for dealing with nonlinear monotone system of equations with convex constraints. The optimal value of the scaling parameter is found by minimizing the condition number of the DFP matrix. Under certain assumptions, the proposed method has global convergence, required minimal storage and is derivative-free. When compared to standard methods, the proposed method requires less iteration, function evaluations, and CPU time. The image restoration test problems demonstrate the method’s reliability and efficiency.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Park Road, Islamabad, 45550, Pakistan

    Maaz ur Rehman & Muhammad Sohaib

  2. Department of Mathematics, Yusuf Maitama Sule University, Kabuga Road, Kano, Nigeria

    Jamilu Sabi’u

  3. Department of Mathematics and Statistics, Bacha Khan University, Charsadda, 24461, Pakistan

    Muhammad Sohaib

  4. Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Muhammad Sohaib & Abdullah Shah

Authors
  1. Maaz ur Rehman
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  2. Jamilu Sabi’u
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  3. Muhammad Sohaib
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  4. Abdullah Shah
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Correspondence to Abdullah Shah.

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ur Rehman, M., Sabi’u, J., Sohaib, M. et al. A projection-based derivative free DFP approach for solving system of nonlinear convex constrained monotone equations with image restoration applications. J. Appl. Math. Comput. 69, 3645–3673 (2023). https://doi.org/10.1007/s12190-023-01897-1

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  • DOI: https://doi.org/10.1007/s12190-023-01897-1

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