A New Conjugate Gradient for Efficient Unconstrained Optimization with Robust Descent Guarantees

The Conjugate Gradient method is a powerful iterative algorithm aims to find the minimum of a function by iteratively searching along conjugate directions. This work presents a nonlinear conjugate gradient approach for unconstrained optimization, resulting from the resolution of a novel optimization problem. The theoretical framework of the proposed method is discussed, and on the application of the descent condition. To evaluate its performance, numerical experiments were conducted, comparing the proposed method against established algorithms () and (Lia and Story) methods. The results demonstrate that the new method not only exhibits enhanced efficiency but also significantly outperforms the () and (Lia and Story) methods in terms of optimization effectiveness. These findings suggest that the proposed approach offers a competitive and promising alternative for solving unconstrained optimization problems.