Double Inertial Proximal Gradient Algorithms for Convex Optimization Problems and Applications

In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.