Modified four-term conjugate gradient method with applications in image restoration and regression problem

Abstract The conjugate gradient (CG) method is recognized for resolving unconstrained optimization problems because of its efficiency, robustness, and minimal memory demands. In this study, a four-term CG method derived from Taylor’s approximation is introduced. The latest modification meets the descent condition, including that required for convergence analysis. The numerical findings demonstrate that the novel 4-term CG method outperforms some highly efficient CG methods, including CG–Descent 6.8. These results are based on tests using more than 180 functions from the CUTEst library across various dimensions. The comparison metrics include the number of iterations, function evaluations, gradient evaluations, and CPU time. The efficacy of the proposed algorithm is further validated through its successful application to two distinct real-world problems: the restoration of images corrupted by Gaussian noise and a regression analysis for predicting future medical appointments. These applications highlight the broad utility of the method in diverse fields, such as image processing and predictive modeling.