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We consider the exact continuous relaxation model of matrix rank minimizationproblem proposed by Yu and Zhang (Comput.Optim.Appl. 1-20, 2022). Motivated bythe inertial techinique, we propose a general inertial smoothing proximalgradient algorithm(GIMSPG) for this kind of problems. It is shown that thesingular values of any accumulation point have a common support set and thenonzero singular values have a unified lower bound. Besides, the zero singularvalues of the accumulation point can be achieved within finite iterations.Moreover, we prove that any accumulation point of the sequence generated by theGIMSPG algorithm is a lifted stationary point of the continuous relaxationmodel under the flexible parameter constraint. Finally, we carry out numericalexperiments on random data and image data respectively to illustrate theefficiency of the GIMSPG algorithm.

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