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中文摘要：
针对含有较大奇异值的矩阵秩最小化问题,采用对数行列式函数代替核范数作为秩函数的非凸近似,应用增广拉格朗日交替方向法求解矩阵秩最小化问题。当罚参数β〉1时,证明此算法产生的迭代序列收敛到原问题的稳定点。最后利用实际数据和随机数据,通过数值实验验证所提出的算法较现有的求解核范数矩阵秩最小化问题的算法更高效。
英文摘要：
To solve the matrix rank minimization problem with large singular values, the log-determinant function was used as a rank approximation instead of the nuclear norm and an augmented Lagrangian alternating direction method was proposed. When penalty parameter β〉1 , the sequence of iterations generated by the proposed algorithm was proved to be convergent to a stationary point of the original problem. Finally, numerical experiments were conducted based on real data and random data. The results demonstrate that the proposed algorithm is more efficient than the existing nuclear norm method in solving the problem of matrix rank minimization.
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