A three-term projection method based on spectral secant equation for nonlinear monotone equations

In this paper, we propose a three-term derivative-free projection algorithm for handling large-scale nonlinear monotone equations with convex constrained. The search direction generated by the proposed algorithm satisfies sufficient descent condition at every iteration. Under some suitable conditions, the global convergence of the algorithm is established. Numerical experiments are provided to show the algorithm is promising and competitive for solving monotone nonlinear equations. In addition, we applied the algorithm to solve signal processing problem arising from compressive sensing.