Applying New Preconditioned Conjugated Gradient Algorithms to  Unconstrained Optimization Problems

Sabreen M. Abbas; Abbas Y. Al-Bayati; Maysoon M. Aziz

doi:10.62383/bilangan.v3i1.378

Authors

Sabreen M. Abbas University of Mosul
Abbas Y. Al-Bayati University of Mosul
Maysoon M. Aziz University of Telafer

DOI:

https://doi.org/10.62383/bilangan.v3i1.378

Keywords:

Preconditioned Conjugate Gradient Algorithms, 3 Analysis, Numerical Optimization Techniques

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.

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