Enhancing Conjugate Gradient Method Through a Novel Investigation Parameter For Unconstrained Minimization

Conjugate gradient algorithms come in a wide range of flavors. The conjugate gradient technique primarily concentrates on the spectral parameter. It follows the standard method proposed by Hastens and Stiefel, In this study, we have devised an innovative approach to spectral conjugate gradient methods we get a new direction conjugate gradient method to solve unconstrained optimization problems, which is based on non-linear function using an inexact line searching introduced a novel direction. In specific scenarios, this groundbreaking direction not only guarantees global convergence but also ensures a downward trajectory. Our numerical experiments unequivocally demonstrate that when compared to traditional CG techniques, depending on the number of functions (NOF), the number of iterations (NOI), and time (CPU), and evaluated using the Dolan-More performance profile, our novel method consistently exhibits superior performance across a diverse set of unconstrained function minimization test. and the convergence condition under some  Hypotheses by using a strong -Wolfe line search.