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In this paper, we consider the exact continuous relaxation model of $l_0$regularization problem which was given by Bian and Chen (SIAM J. Numer. Anal58(1): 858-883, 2020) and propose a smoothing proximal gradient algorithm withextrapolation (SPGE) for this kind of problem. We show that any accumulationpoint of the sequence generated by SPGE algorithm is a lifted stationary pointof the relaxation model for a fairly general choice of extrapolation parameter.Moreover, it is shown that the whole sequence generated by SPGE algorithmconverges to a lifted stationary point of the relaxation model. The convergencerate of $o(\frac{1}{k^{1-\sigma}})(\sigma\in(0,1))$ with respect to squaredproximal residual is established. Finally, we conduct three important numericalexperiments to illustrate the faster efficiency of the SPGE algorithm comparedwith the smoothing proximal gradient(SPG) algorithm proposed by Bian and Chen(SIAM J. Numer. Anal 58(1):858-883, 2020).

The Smoothing Proximal Gradient Algorithm with Extrapolation for the Relaxation of $l_0$ Regularization Problem