A Spectral Perry-Type Derivative Free Method for Solving Nonlinear Equations with Application

This work proposes a Perry-type method to solve large-scale nonlinear equations with convex constraints. The proposed method generates search directions that satisfy a sufficient descent property. An Armijo-type line search strategy is employed to guarantee global convergence of the algorithm. The method is applied to image reconstruction problems, where experimental results show that the reconstructed images attain high PSNR, SNR, and SSIM values, reflecting improved image quality. Numerical results further validate the robustness and computational effectiveness of the proposed method. AMS subject classification: 49J52, 49M15, 65H10, 90C30.