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Mathematics > Optimization and Control

arXiv:2108.03365 (math)
[Submitted on 7 Aug 2021]

Title:Variable metric extrapolation proximal iterative hard thresholding method for $\ell_0$ minimization problem

Authors:Xue Zhang, Xiaoqun Zhang
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Abstract:In this paper, we consider the $\ell_0$ minimization problem whose objective function is the sum of $\ell_0$-norm and convex differentiable function. A variable metric type method which combines the PIHT method and the skill in quasi-newton method, named variable metric extrapolation proximal iterative hard thresholding (VMEPIHT) method, is proposed. Then we analyze its convergence, linear convergence rate and superlinear convergence rate under appropriate assumptions. Finally, we conduct numerical experiments on compressive sensing problem and CT image reconstruction problem to confirm VMPIHT method's efficiency, compared with other state-of-art methods.
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)
MSC classes: 90C26, 90C30
ACM classes: G.1.6
Cite as: arXiv:2108.03365 [math.OC]
  (or arXiv:2108.03365v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2108.03365

Submission history

From: Xue Zhang [view email]
[v1] Sat, 7 Aug 2021 04:49:29 UTC (446 KB)
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