Convergence of Linear Bregman ADMM for Nonconvex and Nonsmooth Problems with Nonseparable Structure
Joint Authors
Jian, Jinbao
Chao, Miantao
Deng, Zhao
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-02-26
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
The alternating direction method of multipliers (ADMM) is an effective method for solving two-block separable convex problems and its convergence is well understood.
When either the involved number of blocks is more than two, or there is a nonconvex function, or there is a nonseparable structure, ADMM or its directly extend version may not converge.
In this paper, we proposed an ADMM-based algorithm for nonconvex multiblock optimization problems with a nonseparable structure.
We show that any cluster point of the iterative sequence generated by the proposed algorithm is a critical point, under mild condition.
Furthermore, we establish the strong convergence of the whole sequence, under the condition that the potential function satisfies the Kurdyka–Łojasiewicz property.
This provides the theoretical basis for the application of the proposed ADMM in the practice.
Finally, we give some preliminary numerical results to show the effectiveness of the proposed algorithm.
American Psychological Association (APA)
Chao, Miantao& Deng, Zhao& Jian, Jinbao. 2020. Convergence of Linear Bregman ADMM for Nonconvex and Nonsmooth Problems with Nonseparable Structure. Complexity،Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1142819
Modern Language Association (MLA)
Chao, Miantao…[et al.]. Convergence of Linear Bregman ADMM for Nonconvex and Nonsmooth Problems with Nonseparable Structure. Complexity No. 2020 (2020), pp.1-14.
https://search.emarefa.net/detail/BIM-1142819
American Medical Association (AMA)
Chao, Miantao& Deng, Zhao& Jian, Jinbao. Convergence of Linear Bregman ADMM for Nonconvex and Nonsmooth Problems with Nonseparable Structure. Complexity. 2020. Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1142819
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1142819