In this paper, we establish a non-convex \(L_{*}-L_{F}\) model for low Tucker rank tensor completion problem. For the new optimization model, three algorithms for solving tensor completion are designed based on the proximal difference of convex algorithm with extrapolation. In theory, the null space property and restricted isometric property condition are discussed and the new bound of restricted isometry constant \(\delta _{2r}\) is given. The optimization objective function is proved to be Kurdyka–Łojasiewicz (KL) function with exponent \( \frac{1}{2}\) . Convergence theory of these algorithms is established, which globally converges to the point of the first-order optimality conditions under KL property. Furthermore, numerical experiments are implemented by these proposed algorithms for the new optimization model and the corresponding algorithms for other models on simulation data and real data. Experimental results show the new models outperform the nuclear norm model and non-convex Schatten p-norm model in precision and CPU times.
