An improved spectral conjugate gradient projection method for monotone nonlinear equations with application

In this paper, we propose an enhanced spectral conjugate gradient (CG) projection method for solving monotone nonlinear equations with application in signal processing. The derivation of the CG parameter involves a combination of the quasi-Newton and the CG search directions, respectively. This integration aims to harness the efficiency of the quasi-Newton direction and the global convergence properties of the CG method, resulting in a more versatile and efficient algorithm. The search direction ensures sufficient descent without relying on any line search, and the global convergence of the proposed method is established under certain conditions. Numerical experiments have been conducted to evaluate the effectiveness of the proposed method. Finally, the proposed method has been applied to address the problems arising in signal reconstruction.