Title: An improved conjugate gradient method for solving unconstrained optimisation and image restoration problems

Authors: Hisham M. Khudhur; Ahmed Amer Mohammad Fawze

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

Abstract: In this paper, we propose an algorithm of hybrid conjugate gradient algorithms that depend on convex combinations using the three-term hybrid conjugated gradient algorithm to solve unconstrained optimisation problems with its application in restoration noisy images. The new parameter is a hybrid Fletcher and Reeves (FR) with the original FR. Finally, a convex combination of the last search direction and a prior iteration's gradient may be used to choose where to search next time. It is clear that the direction of the search was created by a new algorithm that always has the property of descent regardless of the type of line search used and that it is always globally converging some assumptions and using the search line for Wolfe. The numerical results of medium and large dimensions in the smooth nonlinear optimisation functions and the restoration of noisy images help us to show the efficiency and accuracy of the proposed hybrid conjugate gradient algorithm. Even when compared to current approaches, the numerical findings suggest that the proposed methods are more efficient and effective than those now in use.

Keywords: image restoration; Fletcher and Reeves; optimisation; algorithm; smooth.

DOI: 10.1504/IJMMNO.2023.132286

International Journal of Mathematical Modelling and Numerical Optimisation, 2023 Vol.13 No.3, pp.313 - 325

Received: 02 Aug 2022
Accepted: 27 Nov 2022
Published online: 17 Jul 2023 *

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