  In this paper, we consider a non-convex problem which is the sum of
$\ell_0$-norm and a convex smooth function under box constraint. We propose one
proximal iterative hard thresholding type method with extrapolation step used
for acceleration and establish its global convergence results. In detail, the
sequence generated by the proposed method globally converges to a local
minimizer of the objective function. Finally, we conduct numerical experiments
to show the proposed method's effectiveness on comparison with some other
efficient methods.
