Issue |
RAIRO-Oper. Res.
Volume 57, Number 3, May-June 2023
|
|
---|---|---|
Page(s) | 1219 - 1238 | |
DOI | https://doi.org/10.1051/ro/2023065 | |
Published online | 14 June 2023 |
An accelerated proximal alternating direction method of multipliers for robust fused Lasso
1
School of Mathematics and Statistics, Henan University of Science and Technology, Luolong, P.R. China
2
LMIB of the Ministry of Education, School of Mathematical Sciences, Beihang University, Beijing, P.R. China
3
Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI, USA
* Corresponding author: mathshang@sina.com
Received:
1
February
2023
Accepted:
9
May
2023
In the era of big data, much of the data is susceptible to noise with heavy-tailed distribution. Fused Lasso can effectively handle high dimensional sparse data with strong correlation between two adjacent variables under known Gaussian noise. However, it has poor robustness to non-Gaussian noise with heavy-tailed distribution. Robust fused Lasso with l1 norm loss function can overcome the drawback of fused Lasso when noise is heavy-tailed distribution. But the key challenge for solving this model is nonsmoothness and its nonseparability. Therefore, in this paper, we first deform the robust fused Lasso into an easily solvable form, which changes the three-block objective function to a two-block form. Then, we propose an accelerated proximal alternating direction method of multipliers (APADMM) with an additional update step, which is base on a new PADMM that changes the Lagrangian multiplier term update. Furthermore, we give the O(1/K) nonergodic convergence rate analysis of the proposed APADMM. Finally, numerical results show that the proposed new PADMM and APADMM have better performance than other existing ADMM solvers.
Mathematics Subject Classification: 90C25 / 90C30 / 62J05
Key words: Robust fused Lasso / accelerated proximal alternating direction method of multipliers / nonergodic convergence / extension factor
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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