Novel Algorithms with Inertial Techniques for Solving Constrained Convex Minimization Problems and Applications to Image Inpainting

In this paper, we propose two novel inertial forward–backward splitting methods for solving the constrained convex minimization of sum functions, φ1+φ2, in Hilbert spaces and analyze their convergence behavior under some conditions. For first method (iFBS), use operator. The step size depends on a constant Lipschitz continuity ∇φ1, hence weak result proposed is established conditions based fixed point method. With second (iFBS-L), modify method, which independent ∇φ1 by using line search technique introduced Cruz Nghia. As an application these methods, compare efficiency with three-operator (iTOS) them to solve image inpainting problem nuclear norm regularization. Moreover, apply our restoration problems least absolute shrinkage selection operator (LASSO) model, results are compared those (FBS-L) fast iterative shrinkage-thresholding (FISTA).