Derivative-free conjugate residual algorithms for convex constraints nonlinear monotone equations and signal recovery

This paper proposes two new derivative-free algorithms for solving convex constraints nonlinear monotone equations and signal recovery problems arising in compressive sensing. The algorithms combine a three term conjugate residual algorithms for unconstrained optimization problems and the projection technique. The search direction generated by both algorithms, independent of the line search satisfies the sufficient descent condition and are bounded. Convergence of the algorithms was obtained under some assumptions. Finally, numerical examples were reported to show the performance of the algorithms compared with others.