@article{Halilu2025, 
author = {Abubakar Sani Halilu and Mohamad A. Mohamed and Mohammed A. Saleh and Kabiru Ahmed and Abdulgader Z. Almaymuni and Mohammed Y. Waziri and Sulaiman M. Ibrahim and Badr Almutairi},
title = {Accelerated Hager-Zhang type projection scheme for monotone equations with applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {28151-28181},
keywords = {nonlinear monotone equations, convex constraint, conjugate gradient method, sparse signal reconstruction, image de-blurring, image reconstruction, optimization method},
url = {https://www.sciopen.com/article/10.3934/math.20251238},
doi = {10.3934/math.20251238},
abstract = {This paper proposed a new iterative method for solving nonlinear monotone equations with convex constraint and its applications in sparse signal reconstruction and image de-blurring problems. The method can be viewed as an improved adaptation of the generalized Hager-Zhang conjugate gradient method for unconstrained optimization. Unlike the latter which only converged globally for strongly convex functions when the Hager-Zhang parameter        θ    k   lies in the interval        (                  1        4            ,      +      ∞        )  , the new method exhibited this attribute for nonlinear monotone and Lipschitz continuous functions without restriction for        θ    k   under a more relaxed condition. The derivative-free structure of the method made it suitable for both smooth and non-smooth problems. Numerical experiments on benchmark test problems demonstrated the method's superior performance compared to some state-of-the-art algorithms. Furthermore, the algorithm was successfully applied to sparse signal recovery and image de-blurring problems in compressed sensing, confirming its practical effectiveness.}
}