The symmetric ADMM with indefinite proximal regularization and its application
Abstract Due to updating the Lagrangian multiplier twice at each iteration, the symmetric alternating direction method of multipliers (S-ADMM) often performs better than other ADMM-type methods. In practical applications, some proximal terms with positive definite proximal matrices are often added t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-07-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1447-3 |
| _version_ | 1831660809869066240 |
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| author | Hongchun Sun Maoying Tian Min Sun |
| author_facet | Hongchun Sun Maoying Tian Min Sun |
| author_sort | Hongchun Sun |
| collection | DOAJ |
| description | Abstract Due to updating the Lagrangian multiplier twice at each iteration, the symmetric alternating direction method of multipliers (S-ADMM) often performs better than other ADMM-type methods. In practical applications, some proximal terms with positive definite proximal matrices are often added to its subproblems, and it is commonly known that large proximal parameter of the proximal term often results in ‘too-small-step-size’ phenomenon. In this paper, we generalize the proximal matrix from positive definite to indefinite, and propose a new S-ADMM with indefinite proximal regularization (termed IPS-ADMM) for the two-block separable convex programming with linear constraints. Without any additional assumptions, we prove the global convergence of the IPS-ADMM and analyze its worst-case O ( 1 / t ) $\mathcal{O}(1/t)$ convergence rate in an ergodic sense by the iteration complexity. Finally, some numerical results are included to illustrate the efficiency of the IPS-ADMM. |
| first_indexed | 2024-12-19T18:21:23Z |
| format | Article |
| id | doaj.art-ad0c36b6b51f42cd93886bd3f70a86cd |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-19T18:21:23Z |
| publishDate | 2017-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-ad0c36b6b51f42cd93886bd3f70a86cd2022-12-21T20:10:58ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-07-012017112210.1186/s13660-017-1447-3The symmetric ADMM with indefinite proximal regularization and its applicationHongchun Sun0Maoying Tian1Min Sun2School of Sciences, Linyi UniversityDepartment of Physiology, Shandong Coal Mining Health SchoolSchool of Mathematics and Statistics, Zaozhuang UniversityAbstract Due to updating the Lagrangian multiplier twice at each iteration, the symmetric alternating direction method of multipliers (S-ADMM) often performs better than other ADMM-type methods. In practical applications, some proximal terms with positive definite proximal matrices are often added to its subproblems, and it is commonly known that large proximal parameter of the proximal term often results in ‘too-small-step-size’ phenomenon. In this paper, we generalize the proximal matrix from positive definite to indefinite, and propose a new S-ADMM with indefinite proximal regularization (termed IPS-ADMM) for the two-block separable convex programming with linear constraints. Without any additional assumptions, we prove the global convergence of the IPS-ADMM and analyze its worst-case O ( 1 / t ) $\mathcal{O}(1/t)$ convergence rate in an ergodic sense by the iteration complexity. Finally, some numerical results are included to illustrate the efficiency of the IPS-ADMM.http://link.springer.com/article/10.1186/s13660-017-1447-3symmetric alternating direction method of multipliersindefinite proximal regularizationglobal convergence |
| spellingShingle | Hongchun Sun Maoying Tian Min Sun The symmetric ADMM with indefinite proximal regularization and its application Journal of Inequalities and Applications symmetric alternating direction method of multipliers indefinite proximal regularization global convergence |
| title | The symmetric ADMM with indefinite proximal regularization and its application |
| title_full | The symmetric ADMM with indefinite proximal regularization and its application |
| title_fullStr | The symmetric ADMM with indefinite proximal regularization and its application |
| title_full_unstemmed | The symmetric ADMM with indefinite proximal regularization and its application |
| title_short | The symmetric ADMM with indefinite proximal regularization and its application |
| title_sort | symmetric admm with indefinite proximal regularization and its application |
| topic | symmetric alternating direction method of multipliers indefinite proximal regularization global convergence |
| url | http://link.springer.com/article/10.1186/s13660-017-1447-3 |
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