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Optimization of unconstrained problems using a developed algorithm of spectral conjugate gradient method calculation

Author

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  • Mrad, Hatem
  • Fakhari, Seyyed Mojtaba

Abstract

This paper presents a numerical investigation of the spectral conjugate directions formulation for optimizing unconstrained problems. A novel modified algorithm is proposed based on the conjugate gradient coefficient method. The algorithm employs the Wolfe inexact line search conditions to determine the optimum step length at each iteration and selects the appropriate conjugate gradient coefficient accordingly. The algorithm is evaluated through several numerical experiments using various unconstrained functions. The results indicate that the algorithm is highly stable, regardless of the starting point, and has better convergence rates and efficiency compared to classical methods in certain cases. Overall, this research provides a promising approach to solving unconstrained optimization problems.

Suggested Citation

  • Mrad, Hatem & Fakhari, Seyyed Mojtaba, 2024. "Optimization of unconstrained problems using a developed algorithm of spectral conjugate gradient method calculation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 282-290.
    • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:282-290
    DOI: 10.1016/j.matcom.2023.07.026
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    References listed on IDEAS

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    1. Farid, Mahboubeh, 2016. "Accelerated diagonal gradient-type method for large-scale unconstrained optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 24-30.
    2. Rivaie, Mohd & Mamat, Mustafa & Abashar, Abdelrhaman, 2015. "A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1152-1163.
    3. Abubakar, Auwal Bala & Kumam, Poom & Malik, Maulana & Ibrahim, Abdulkarim Hassan, 2022. "A hybrid conjugate gradient based approach for solving unconstrained optimization and motion control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 640-657.
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