Convergence of iterative hard-thresholding algorithm with continuation

Tao Sun, Lizhi Cheng

Abstract: In this paper, we study the convergence of iterative hard-thresholding algorithm with continuation for solving the $$\ell ^0$$ ℓ 0 -regularized minimization. A decreasing continuation strategy is used for the regularization parameter. By using the Kurdyka–Łojasiewicz property, we prove that the algorithm globally converges to a critical point of a known objective function. Numerical results are also presented.