An Enhanced Conjugate Gradient Algorithm for Solving Unconstrained Optimization and Image Restoration Problems

In order to address unconstrained optimization problems, conjugate gradient methods are frequently employed. When considering the unconstrained optimization issue, the accelerated conjugate gradient approach yields better numerical results than the conjugate gradient method. In this study, we introduce a modified conjugate gradient method that uses Wolfe line search to determine the direction of descent. We prove that the proposed method is globally convergent in modest settings. Numerical evidence indicates the significance of the proposed technique for our test functions. and also that the algorithm’s effectiveness is further validated through its application to image restoration problems, where it achieves superior results in terms of peak signal-to-noise ratio and structural similarity index measure.