Asian Journal of Pure and Applied Mathematics

The Strong Wolfe line search conditions are widely recognized for providing robust theoretical convergence guarantees in nonlinear conjugate gradient (CG) methods, yet their practical efficacy compared to simpler inexact line searches remains underexplored for large-scale optimization. This study presents a comprehensive numerical evaluation of eight classical CG methods, BAN, FR, PRP, HS, CD, DY, LS, and HZ, under the Strong Wolfe line search framework. Through extensive experiments on 50 high-dimensional benchmark problems (n = 5,000 and 10,000) from the CUTEr collection, we assess convergence rates, computational efficiency, and robustness using rigorous statistical analysis. Results indicate that the Polak–Ribière–Polyak (PRP) method achieves the highest success rate (88%) and statistical dominance, followed by Liu–Storey (LS) at 78% and Hager–Zhang (HZ) at 70%. A novel comparative analysis with prior Armijo-based findings reveals that Strong Wolfe improves stability for methods like HS and DY but introduces computational overhead that erodes performance gains for LS and HZ. Statistical significance testing (Wilcoxon signed-rank, α=0.05) confirms PRP's superiority over all other methods under Strong Wolfe conditions. However, Strong Wolfe introduces 12–38% computational overhead compared to Armijo, highlighting a trade-off between convergence reliability and efficiency. This work provides the first comprehensive benchmarking of classical CG methods under uniform Strong Wolfe conditions, offering actionable insights and a decision framework for practitioners in selecting appropriate line search strategies for large-scale unconstrained optimization problems.