A new spectral conjugate gradient method for unconstrained optimization and its application in neural networks

‎This work introduces a new variation of the Hestenes and Stiefel nonlinear conjugate gradient (HS) method by combining the advantages of the spectral conjugate gradient method and the conjugacy condition of the quasi-Newton method‎. ‎The proposed method incorporates inexact line searches and categorizing it as a descent method‎. ‎By employing line searches that satisfy the Wolfe conditions‎, ‎we establish sufficient descent properties and global convergence condition‎, ‎assuming that the appropriate conditions are met‎. ‎Additionally‎, ‎we perform numerical experiments utilizing benchmark functions frequently used in optimization assignments to evaluate the effectiveness of the proposed method‎. ‎The results demonstrate that our method outperforms the traditional HS method‎. ‎Furthermore‎, ‎we successfully implement the newly developed technique to train neural networks (NNs)‎, ‎demonstrating its practicality for non-traditional optimization tasks‎.