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In this paper, we propose a derivative free algorithm for solving non-linear monotone equations with convex constraints. The proposed algorithm combines the method of spectral gradient and the projection method. We also modify the backtracking line search technique. The global convergence of the proposed method is guaranteed, under the mild conditions. Further, the numerical experiments show that the large-scale non-linear equations with convex constraints can be effectively solved with our method. The L<sub>1</sub>-norm regularized problems in signal reconstruction are studied by using our method.

A Modified Spectral Gradient Projection Method for Solving Non-Linear Monotone Equations With Convex Constraints and Its Application