An improved descent hybrid gradient-based projection algorithm for nonlinear equations and signal recovery problems

Derivative-free projection methods for solving nonlinear monotone equations have recently gained favor with researchers. Based on a hybrid conjugate gradient algorithm and the projection techniques, in this work, we present a descent derivative-free projection method for finding solutions to large-scale nonlinear monotone equations. The proposed method satisfies the descent condition and, under some suitable assumptions, its global convergence is established. The presented method’s efficacy is demonstrated through numerical experiments. Results show that, compared to other methods with similar structure, the method performs better. The method is further applied to an application in signal recovery, and it is proving to be efficient.