A hybrid spectral projection-based method for solving monotone nonlinear systems and signal recovery

In this paper, we propose a hybrid spectral gradient algorithm for solving the constrained nonlinear monotone systems with an application to signal recovery. The proposed algorithm is a convex combination of the well-known spectral parameters. An efficient formula for computing the convex hybridization parameter is also proposed by tending the proposed direction to approach the generalized quasi-Newton direction. The global convergence of this algorithm is shown using the monotone and Lipschitz continuous assumptions. Finally, a numerical comparison with other related algorithms demonstrated that the suggested algorithm outperformed them regarding iterations, function evaluation, and computational time.