提出了一种新的张量补全模型，即用光滑$\epsilon$-迹函数来代替核范数的双层优化模型。在新模型中，不需要在每次迭代时对张量的所有模式矩阵进行奇异值分解，最多需要两次奇异值分解，有效减少了张量全部模展开带来的较大计算量，提高了计算效率。最后，通过随机张量补全和图像修复的数值实验结果表明，与传统的核范数模型相比，所提出的极小极小和极小极大组合模型双层优化具有较少的CPU时间和较好的精度。

In this paper, the novel optimization model for tensor completion by considering the bi-level optimization model with the smooth $\epsilon$-trace functions instead of nuclear norm is proposed. In the new model, it is not necessary to perform singular value decomposition for all modes of the tensor in each iteration, but only two singular value decomposition is needed at most, which effectively reduces the huge computation amount brought by all modes expansion of the tensor and greatly improves the computation efficiency. Finally, the experimental results of randomly generated tensor completion problem and color image inpainting problem show that the proposed bi-level (minimin and minimax combination) optimization models usually has less than CPU time and better precision than the traditional nuclear norm based model.