<p>This paper presents an enhanced Wei-Yao-Liu conjugate gradient projection algorithm, tailored for solving large-scale nonlinear convex constrained monotone equations. The algorithm’s search direction guarantees sufficient descent, while both the direction and line search are derivative-free, making it highly efficient for large-scale problems. We prove the algorithm’s global convergence under suitable assumptions and demonstrate its applicability to sparse signal reconstruction and blurry image recovery in compressive sensing. Numerical experiments validate the algorithm’s effectiveness, especially in large-scale scenarios, underscoring the advantages of its derivative-free design.</p>