General inertial smoothing proximal gradient algorithm for the relaxation of matrix rank minimization problem

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.