A modified PRP-type derivative-free projection algorithm for constrained nonlinear equations with applications

In this paper, we propose a novel derivative-free projection algorithm based on the classical Polak–Ribiére–Polyak (PRP) method. This algorithm designs a search direction with sufficient descent and trust region properties, integrating an efficient line search approach and projection techniques. Under standard assumptions, the global convergence of the proposed algorithm is established. Numerical experiments demonstrate that the proposed algorithm outperforms two existing algorithms in terms of efficiency and robustness, and is successfully applied to sparse signal recovery and image denoising problems.