A projection method for solving monotone nonlinear equations with application

Abstract

Abstract Nonlinear equations are one of the most trending research areas due to their vast applications in the sciences, social sciences, and engineering. However, the conjugate gradient method (CG) is one of the most rapidly developing iterative techniques for solving nonlinear monotone problems. Recently, much work has been done on using the CG method to solve monotone nonlinear equations. This paper discusses a new variant for solving constrained monotone nonlinear equations. The method satisfies the sufficient descent condition and proves global convergence and R-linear convergence with the help of some reasonable assumptions. In addition, two sets of numerical tests were conducted. The first experiment shows the good performance of the proposed method compared to existing methods, while the second experiment displays the performance of the proposed algorithm in compressive sensing.