Numerical optimization of large-scale monotone equations using the free-derivative spectral conjugate gradient method

This study introduced an efficient method for solving non-linear equations. Our approach enhances the traditional spectral conjugate gradient parameter, resulting in significant improvements in the resolution of complex nonlinear problems. This innovative technique ensures global convergence and descent condition supported by carefully considered assumptions. The efficiency and effectiveness of the proposed method is highlighted by its outstanding numerical performance. To validate our claims, large-scale numerical simulations were conducted. These tests were designed to evaluate the capabilities of our proposed algorithm rigorously. In addition, we performed a comprehensive comparative numerical analysis, benchmarking our method against existing techniques. This analysis revealed that our approach consistently outperformed others in terms of theoretical robustness and numerical efficiency. The superiority of our method is evident in its ability to solve large-scale problems with accuracy in function evaluations, fewer iterations, and improved computational performance thereby, making it a valuable contribution to the field of numerical optimization.