A modified RMIL conjugate gradient-based projection algorithm for constrained nonlinear equations: application to image denoising

In this paper, a modified Rivaie-Mohd-Ismail-Leong (RMIL) conjugate gradient-based projection algorithm for constrained nonlinear equations is proposed, which integrates projection techniques and line search approaches to enhance solution accuracy and efficiency. The key characteristics of the proposed algorithm are as follows: (i) the search direction is designed to ensure both sufficient descent property and trust region feature; (ii) the global convergence of the proposed algorithm is proven without the need for a Lipschitz continuity condition; (iii) extensive experiments demonstrate that the proposed algorithm is both effective and competitive, particularly in solving large-scale constrained nonlinear equations and image denoising problems, where it outperforms some existing methods in the literature.