A modified three-term of Dai–Yuan type derivative-free algorithm for nonlinear monotone equations with signal recovery problems

A lot of researchers have introduced iterative schemes for solving convex constrained nonlinear monotone equations. This paper aims to propose a modified three-term of Dai–Yuan type (TTDY) derivative-free algorithm for nonlinear monotone equations. The presented method has a low storage requirement, it can therefore easily solve large scale nonlinear equations. At every iteration, it generates a descent search direction independent of the line search. We established the global convergence of the propose approach under standard conditions. Numerical examples are given to illustrate the effectiveness of the algorithm when solving large-scale nonlinear monotone equations. Finally, the capacity of the proposed algorithm has been tested to solve nonlinear monotone equations equivalent to the ${\ell }_1$-norm regularized minimization problem.