Convergence analysis of a three-term extended RMIL CGP-based algorithm for constrained nonlinear equations and image denoising applications

With a focus on image denoising applications, this paper proposed a three-term extended Rivaie-Mustafa-Ismail-Leong (RMIL) conjugate gradient projection (CGP)-based algorithm for solving constrained nonlinear equations. Unlike traditional methods, the proposed algorithm relied only on the continuity and monotonicity properties of the nonlinear equations, and did not require the more restrictive Lipschitz continuity condition. A rigorous convergence analysis was established under these relaxed assumptions. At the algorithmic level, a novel three-term search direction was constructed by extending previous two-term schemes through the introduction of a carefully designed scale factor, which effectively eliminates the need for a line search procedure. Comprehensive numerical experiments on standard benchmark problems demonstrated the algorithm's efficiency and competitiveness, consistently outperforming comparable three-term algorithms in terms of running time in seconds, number of iterations, and function evaluations. Furthermore, the proposed algorithm has been successfully applied to image denosing problems.