论文标题
一般惯性平滑近端梯度算法，用于放松基质等级最小化问题
General inertial smoothing proximal gradient algorithm for the relaxation of matrix rank minimization problem
论文作者
论文摘要
我们考虑了Yu和Zhang提出的矩阵秩最小化问题的确切连续放松模型（comput.optim.appl。1-20，2022）。在惯性的techinique中，我们提出了这种问题的一般惯性平滑近端梯度算法（GIMSPG）。结果表明，任何积累点的奇异值都有一个共同的支持集，而非零的单数值具有统一的下限。此外，在有限的迭代中可以实现累积点的零单数值。此外，我们证明，GIMSPG算法生成的序列的任何积累点都是在灵活参数约束下连续弛豫模型的固定点。最后，我们分别对随机数据和图像数据进行数值实验，以说明GIMSPG算法的效率。
We consider the exact continuous relaxation model of matrix rank minimization problem proposed by Yu and Zhang (Comput.Optim.Appl. 1-20, 2022). Motivated by the inertial techinique, we propose a general inertial smoothing proximal gradient algorithm(GIMSPG) for this kind of problems. It is shown that the singular values of any accumulation point have a common support set and the nonzero singular values have a unified lower bound. Besides, the zero singular values of the accumulation point can be achieved within finite iterations. Moreover, we prove that any accumulation point of the sequence generated by the GIMSPG algorithm is a lifted stationary point of the continuous relaxation model under the flexible parameter constraint. Finally, we carry out numerical experiments on random data and image data respectively to illustrate the efficiency of the GIMSPG algorithm.
