An improved conjugate gradient algorithm by adapting a new line search technique

The conjugate gradient (CG) method is an optimization technique known for its rapid convergence; it has blossomed into significant developments and applications. Numerous variations of CG methods have emerged to enhance computational efficiency and address real-world challenges. This work presents a new conjugate gradient method for solving nonlinear unconstrained optimization problems by introducing a new conjugate gradient parameter. To improve the convergence properties, we have proposed a new inexact line search technique that fits in with the suggested approach and can also be useful for other gradient descent methods. The existence of a steplength that meets the new line search conditions is established. The generated descent direction and the convergence properties of the suggested approach are studied under the new line search conditions, where the global convergence is proven under mild assumptions. The proposed approach is evaluated on various test functions, and a comparison with recent similar algorithms is carried out. Furthermore, the proposed algorithm is applied for restoring images with different noise levels.