An accelerated proximal iterative hard thresholding method for ℓ₀ minimization

2017/09/06 by Zhang, Xue, Zhang, Xiaoqun
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1709.01668

Abstract

In this paper, we consider a non-convex problem which is the sum of ℓ₀-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.

Related

• Proximal Iterative Hard Thresholding Algorithm for Sparse Group ℓ₀-Regularized Optimization with Box Constraint
• Smoothing fast iterative hard thresholding algorithm for ℓ₀ regularized nonsmooth convex regression problem
• Iterative Hard Thresholding Methods for l₀ Regularized Convex Cone Programming
• Variable metric extrapolation proximal iterative hard thresholding method for ℓ₀ minimization problem
• The fastest ℓ_1,∞ prox in the west