Tensor Completion via Minimum and Maximum Optimization with Noise

In this paper, a novel optimization model for solving tensor completion with noise is proposed, whose objective function is a convex combination of the minimum nuclear norm and maximum nuclear norm. The necessary and sufficient conditions of the stationary point and optimal solution are discussed. Based on the proximal gradient algorithm and feasible direction method, we design a new algorithm for solving the proposed nonconvex and nonsmooth optimization problem and prove that the subsequence generated by the new algorithm converges to the stationary point. Finally, experimental results on random sample completions and image data show that the proposed optimization model and algorithm outperform the compared algorithms in terms of CPU time or precision.