Improved Dai–Liao Conjugate Gradient Methods for Large-Scale Unconstrained Optimization

This research introduces and evaluates two enhanced conjugate gradient methods for unconstrained optimization, building upon the DaiLiao conjugacy condition and further refined through the application of Taylor series expansion. These novel methodologies were rigorously compared against the classical Hestenes-Stiefel (HS) method using a diverse suite of benchmark test functions. The numerical results obtained unequivocally demonstrate a significant improvement in computational efficiency achieved by the proposed methods. Notably, our enhanced methods consistently outperformed the HS method across several critical performance metrics, including a reduction in the number of iterations required for convergence, a decrease in the total number of function evaluations, and an overall faster computation time