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

Abstract

The conjugate gradient method (CG) is one of the most rapidly expanding and efficient ways of solving unconstrained minimization problems. Recently, there has been a lot of effort put into extending the CG approach to solve monotone nonlinear equations. In this paper, we describe a variation of the CG method for solving constrained monotone nonlinear equations. 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 sparse signal reconstruction.