Title: A new three-term conjugate gradient method for unconstrained optimisation and its applications in image restoration

Authors: Hisham M. Khudhur; Hind H. Mohammed

Addresses: Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq ' Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

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.

Keywords: algorithms; CG; optimisation; FR and TTFR; restoration; three-term Fletcher and Reeves; TTFR.

DOI: 10.1504/IJMOR.2024.138901

International Journal of Mathematics in Operational Research, 2024 Vol.28 No.2, pp.253 - 273

Received: 25 Mar 2023
Accepted: 02 Apr 2023
Published online: 03 Jun 2024 *

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