Global convergence via modified self-adaptive approach for solving constrained monotone nonlinear equations with application to signal recovery problems

The conjugate gradient method (CG) is one of the most rapidly expanding and efficient ways for solving the unconstrained minimization problems. Recently, there has been a lot of effort into extending the CG approach to solve monotone nonlinear equations. For constrained monotone nonlinear equations, we describe a variation of the proposed method in this paper. The approach has a sufficient descent property, and its global convergence has been demonstrated with the help of some reasonable assumptions. Two sets of numerical tests were run to demonstrate the proposed method’s superior performance when compared to other methods. The initial experiment aimed to solve nonlinear equations with constraints, while in the second experiment, the method was applied to signal processing as well as issues with image recovery.