A spectral Conjugate Gradient method for solving unconstrained optimization problems

The conjugate gradient (CG) method stands out as one of the most rapidly growing and effective approaches for addressing unconstrained optimization problems.In recent years, significant efforts have been dedicated to adapting the CG for tackling nonlinear optimization challenges.This research article introduces a new modification of the Fletcher-Reeves (FR) conjugate gradient method.The proposed method is characterized by its sufficient descent property, and its global convergence has been established under specific assumptions.Numerical experiments conducted on 96 functions from the CUTEr collection demonstrate the potential and effectiveness of the proposed methods.The computational results show that the proposed MFR method achieves better performance in terms of function and gradient evaluations as well as CPU time compared to DPRP and FR, while remaining competitive with NPRP.These findings confirm that enforcing the sufficient descent condition in equality form can provide both theoretical robustness and practical efficiency.