A parameterized three-operator splitting algorithm for non-convex minimization problems with applications

In this paper, we propose a parameterized three-operator splitting algorithm to solve nonconvex minimization problems with the sum of three non-convex functions, where two of them have Lipschitz continuous gradients.We establish the convergence of the proposed algorithm under the Kurdyka-Łojasiewicz assumption by constructing a suitable energy function with a non-increasing property.As applications, we employ the proposed algorithm to solve low-rank matrix recovery and image inpainting problems.Numerical results demonstrate the efficiency and effectiveness of the proposed algorithm compared to other algorithms.