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All Journal Bilangan: Jurnal Ilmiah Matematika, Kebumian dan Angkasa
Abbas Y. Al-Bayati
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Astronomy Mathematics

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Applying New Preconditioned Conjugated Gradient Algorithms to Unconstrained Optimization Problems Sabreen M. Abbas; Abbas Y. Al-Bayati; Maysoon M. Aziz
Bilangan : Jurnal Ilmiah Matematika, Kebumian dan Angkasa Vol. 3 No. 1 (2025): Bilangan : Jurnal Ilmiah Matematika, Kebumian dan Angkasa
Publisher : Asosiasi Riset Ilmu Matematika dan Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/bilangan.v3i1.378

Abstract

In this paper, we study a new and improved preconditioned conjugate gradient (PCG) algorithm based on Dai and Liao's procedure to enhance the CG algorithm of (Maulana). The new PCG algorithm satisfies the coupling condition and the sufficient descent condition. This work proposes improved conjugate gradient methods to enhance the efficiency and robustness of classical conjugate gradient methods. The study changes the diagonal of the inverse Hessian approximation to quasi-Newton Broyden-Fletcher-Goldfarb-Shano (BFGS) updating to make a preconditioner for nonlinear conjugate gradient (NCG) methods used to solve large-scale optimization problems with no constraints. We will calculate the step size of this two-term algorithm by accelerating the Wolfe-Powell line searching technique. The proposed new PCG algorithms have proven their global convergence in certain specific conditions reported in this paper.
Co-Authors Maysoon M. Aziz Sabreen M. Abbas