Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem
The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving various nonconvex consensus problem. The convergence of the conventional ADMM (i.e., 2-block) for convex objective functions has been stated for a long time. As an accelerated techni...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/4316267 |
| _version_ | 1797852235691982848 |
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| author | Yang Liu Yazheng Dang |
| author_facet | Yang Liu Yazheng Dang |
| author_sort | Yang Liu |
| collection | DOAJ |
| description | The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving various nonconvex consensus problem. The convergence of the conventional ADMM (i.e., 2-block) for convex objective functions has been stated for a long time. As an accelerated technique, the inertial effect was used by many authors to solve 2-block convex optimization problem. This paper combines the ADMM and the inertial effect to construct an inertial alternating direction method of multipliers (IADMM) to solve the multiblock nonconvex consensus problem and shows the convergence under some suitable conditions. Simulation experiment verifies the effectiveness and feasibility of the proposed method. |
| first_indexed | 2024-04-09T19:30:47Z |
| format | Article |
| id | doaj.art-3d1924fa8a0a4b598ff160e25c68b3bb |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-04-09T19:30:47Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-3d1924fa8a0a4b598ff160e25c68b3bb2023-04-05T00:00:04ZengHindawi LimitedJournal of Mathematics2314-47852023-01-01202310.1155/2023/4316267Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus ProblemYang Liu0Yazheng Dang1Department of Information Science and TechnologySchool of ManagementThe alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving various nonconvex consensus problem. The convergence of the conventional ADMM (i.e., 2-block) for convex objective functions has been stated for a long time. As an accelerated technique, the inertial effect was used by many authors to solve 2-block convex optimization problem. This paper combines the ADMM and the inertial effect to construct an inertial alternating direction method of multipliers (IADMM) to solve the multiblock nonconvex consensus problem and shows the convergence under some suitable conditions. Simulation experiment verifies the effectiveness and feasibility of the proposed method.http://dx.doi.org/10.1155/2023/4316267 |
| spellingShingle | Yang Liu Yazheng Dang Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem Journal of Mathematics |
| title | Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem |
| title_full | Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem |
| title_fullStr | Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem |
| title_full_unstemmed | Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem |
| title_short | Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem |
| title_sort | convergence analysis of multiblock inertial admm for nonconvex consensus problem |
| url | http://dx.doi.org/10.1155/2023/4316267 |
| work_keys_str_mv | AT yangliu convergenceanalysisofmultiblockinertialadmmfornonconvexconsensusproblem AT yazhengdang convergenceanalysisofmultiblockinertialadmmfornonconvexconsensusproblem |