低秩稀疏矩阵恢复的快速非单调交替极小化方法

针对低秩稀疏矩阵恢复问题的一个非凸优化模型，本文提出了一种快速非单调交替极小化方法.主要思想是对低秩矩阵部分采用交替极小化方法，对稀疏矩阵部分采用非单调线搜索技术来分别进行迭代更新.非单调线搜索技术是将单步下降放宽为多步下降，从而提高了计算效率.文中还给出了新算法的收敛性分析.最后，通过数值实验的比较表明，矩阵恢复的非单调交替极小化方法比原单调类方法更有效.

FAST ALTERNATING MINIMIZATION METHOD WITH NON-MONOTONE SEARCH FOR LOW-RANK AND SPARSE MATRIX RECOVERY

In this paper, we propose a fast alternating minimization method with non-monotone line search technique for a non-convex optimization model of low-rank and sparse matrix recovery problem. The main idea is to use the alternating minimization method for the low-rank matrix part, and use the non-monotone line search technique for the sparse matrix part to iteratively update, respectively. The non-monotone line search technique relaxes the single-step descent into a multi-step descent, which greatly improves the computational efficiency. The paper also gives the convergence analysis of the new algorithm. Finally, the comparison of numerical experiments show that the alternate minimization method of the non-monotone technique of matrix recovery is more effective than the original monotone method.