A New Proximal Iterative Hard Thresholding Method with Extrapolation for $$\ell _0$$ ℓ 0 Minimization

Abstract

In this paper, we consider a non-convex problem which is the sum of $$\ell _0$$ -norm and a convex smooth function under a box constraint. We propose one proximal iterative hard thresholding type method with an extrapolation step 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.