Abstract

In this paper, we propose a regularized alternating direction method of multipliers (RADMM) for a class of nonconvex optimization problems. The algorithm does not require the regular term to be strictly convex. Firstly, we prove the global convergence of the algorithm. Secondly, under the condition that the augmented Lagrangian function satisfies the Kurdyka–Łojasiewicz property, the strong convergence of the algorithm is established. Finally, some preliminary numerical results are reported to support the efficiency of the proposed algorithm.

Details

Title
A regularized alternating direction method of multipliers for a class of nonconvex problems
Author
Jin Bao Jian 1 ; Zhang, Ye 2 ; Mian Tao Chao 2   VIAFID ORCID Logo 

1  College of Mathematics and Information Science, Guangxi University, Nanning, China; College of Science, Guangxi University for Nationalities, Nanning, China 
2  College of Mathematics and Information Science, Guangxi University, Nanning, China 
Pages
1-16
Publication year
2019
Publication date
Jul 2019
Publisher
Springer Nature B.V.
ISSN
10255834
e-ISSN
1029242X
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1186/s13660-019-2145-0
ProQuest document ID
2256508062
Copyright
Journal of Inequalities and Applications is a copyright of Springer, (2019). All Rights Reserved., © 2019. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.