An accelerated proximal iterative hard thresholding method for $\ell_0$ minimization

TL;DR

This paper introduces an accelerated proximal iterative hard thresholding method for solving non-convex $\, ext{ extlbrackdbl}0 ext{ extrbrackdbl}$-norm minimization problems with box constraints, demonstrating global convergence and superior performance.

Contribution

The paper proposes a novel accelerated proximal iterative hard thresholding algorithm with convergence guarantees for $\, ext{ extlbrackdbl}0 ext{ extrbrackdbl}$ minimization under box constraints.

Findings

The method converges globally to a local minimizer.

Numerical experiments show improved efficiency over existing methods.

The approach effectively handles non-convex $\, ext{ extlbrackdbl}0 ext{ extrbrackdbl}$ problems.

Abstract

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.