  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.
