一种求解低秩矩阵补全的修正加速近端梯度算法

A Modified Accelerated Proxomal Gradient Algorithm for Low-rank Matrix Completion

设计适应大规模数据的快速算法是求解低秩矩阵补全的重点。文章改变了加速近端梯度算法的步长,对近似函数的近端最优点和上一迭代点增加了一个仿射组合。通过控制仿射系数,能够使得到的新迭代点有靠近原函数的趋势,进而能在保持算法精度的同时提高算法效率。最后通过相应的数值实验证明了算法的有效性和稳定性。

It is important to design a fast algorithm to adapt to large-scale data to solve the low-rank matrix completion.In this paper,by changing the step size of the accelerated proximal gradient algorithm,an affine combination is added to the proximal best point of the approximate function and the last iteration point.By controlling the affine coefficient,the new iteration points can be made close to the original function,which can improve the efficiency of the algorithm while maintaining the simple accuracy.The global convergence analysis is also given.Finally,the effectiveness and stability of the proposed algorithm are proved by numerical experiments.