A Parallel Splitting Augmented Lagrangian Method for Two-Block Separable Convex Programming with Application in Image Processing
The augmented Lagrangian method (ALM) is one of the most successful first-order methods for convex programming with linear equality constraints. To solve the two-block separable convex minimization problem, we always use the parallel splitting ALM method. In this paper, we will show that no matter h...
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| Vydáno v: | Mathematical problems in engineering Ročník 2020; číslo 2020; s. 1 - 10 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cairo, Egypt
Hindawi Publishing Corporation
2020
Hindawi John Wiley & Sons, Inc |
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| ISSN: | 1024-123X, 1563-5147 |
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| Abstract | The augmented Lagrangian method (ALM) is one of the most successful first-order methods for convex programming with linear equality constraints. To solve the two-block separable convex minimization problem, we always use the parallel splitting ALM method. In this paper, we will show that no matter how small the step size and the penalty parameter are, the convergence of the parallel splitting ALM is not guaranteed. We propose a new convergent parallel splitting ALM (PSALM), which is the regularizing ALM’s minimization subproblem by some simple proximal terms. In application this new PSALM is used to solve video background extraction problems and our numerical results indicate that this new PSALM is efficient. |
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| AbstractList | The augmented Lagrangian method (ALM) is one of the most successful first-order methods for convex programming with linear equality constraints. To solve the two-block separable convex minimization problem, we always use the parallel splitting ALM method. In this paper, we will show that no matter how small the step size and the penalty parameter are, the convergence of the parallel splitting ALM is not guaranteed. We propose a new convergent parallel splitting ALM (PSALM), which is the regularizing ALM’s minimization subproblem by some simple proximal terms. In application this new PSALM is used to solve video background extraction problems and our numerical results indicate that this new PSALM is efficient. |
| Author | Liu, Jing Wang, Tonghui Duan, Yongrui |
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| CitedBy_id | crossref_primary_10_1109_TGRS_2022_3172018 crossref_primary_10_1155_2022_8054688 |
| Cites_doi | 10.1093/imanum/drt060 10.1137/100781894 10.1137/090777761 10.1007/s10589-015-9736-6 10.1137/130922793 10.1016/j.cam.2018.07.007 10.1016/j.cosrev.2014.04.001 10.1137/s1064827596304010 10.1007/s10589-015-9770-4 10.1007/s11263-013-0611-6 10.1109/tpami.2011.282 10.1007/bf00927673 10.1137/080738970 10.1007/s11263-012-0515-x 10.1137/060657704 |
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| Copyright | Copyright © 2020 Jing Liu et al. Copyright © 2020 Jing Liu et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. http://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Convergence Convexity Image processing Mathematical problems Nonlinear programming Optimization Splitting |
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| Title | A Parallel Splitting Augmented Lagrangian Method for Two-Block Separable Convex Programming with Application in Image Processing |
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