Tensor Completion via Minimum and Maximum Optimization with Noise

Abstract

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