A new three-term conjugate gradient method for unconstrained optimisation and its applications in image restoration Online publication date: Mon, 03-Jun-2024
by Hisham M. Khudhur; Hind H. Mohammed
International Journal of Mathematics in Operational Research (IJMOR), Vol. 28, No. 2, 2024
Abstract: Conjugate gradient methods (CGM) are generally used to solve unconstrained optimisation problems. In this research, the three-term CGM was developed depending on the conjugate coefficient of the Fletcher and Reeves (FR) conjugate descent method and the second condition of the Wolfe's strong search line, and the strong Wolfe condition was used to obtain the step length. According to some assumptions, the properties of descent and global convergence have been achieved for the new proposed method. Finally, we used the proposed method to solve the unconstrained optimisation functions to show its efficiency, and it was actually superior to the FR and three-term Fletcher and Reeves (TTFR) methods. Hence, we used the proposed new conjugate gradient algorithm in image restoration and image denoising. According to the numerical results, the recently proposed algorithm outperforms both FR and Fletcher and Reeves (TTFR) algorithms.
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