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Paper details
Number 2 - June 2025
Volume 35 - 2025
A combination of two conjugate gradient methods under a new line search with its application in image restoration problems
Asma Maiza, Raouf Ziadi, Mohammed A. Saleh, Abdulgader Z. Almaymuni
Abstract
A combined conjugate gradient algorithm is introduced for solving unconstrained optimization problems. In the suggested
approach, the conjugate gradient parameter is defined as a combination of PRP (Polak-Ribiére-Polyak) and BRB (Rahali-
Belloufi-Benzine) conjugate gradient parameters. To improve the convergence properties, we have adopted a new inexact
line search technique that fits in with the suggested approach. The proposed line search technique can be useful for other
gradient descent methods. We have established the existence of a step length that meets the new line search conditions. The
generated descent direction and the convergence properties of the suggested approach are studied under the new line search
conditions and the proposed method converges globally under mild assumptions. Our approach is evaluated on various test
functions, and a comparison with similar recent algorithms is carried out. Furthermore, the proposed algorithm is applied
for restoring images with different noise levels.
Keywords
unconstrained optimization, conjugate gradient methods, inexact line search, global convergence, image processing