A Relaxed Alternating Direction Method Of Multipliers For Separable Nonconvex Minimization Problems

The alternating direction method of multipliers (ADMM) is popular and powerful in computing the solutions of various composite minimization problems with constraints. In this paper, we propose a relaxed ADMM with a general dual step-size, which includes the classic ADMM in the algorithm framework, f...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 207; no. 1; p. 17
Main Authors: Zhao, Jing, Guo, Chenzheng, Qin, Xiaolong
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.10.2025
Subjects:
Algorithms
Constraints
Convex analysis
Lagrange multiplier
Multipliers
Optimization
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:The alternating direction method of multipliers (ADMM) is popular and powerful in computing the solutions of various composite minimization problems with constraints. In this paper, we propose a relaxed ADMM with a general dual step-size, which includes the classic ADMM in the algorithm framework, for minimizing separable nonconvex functions with linear constraints. Under some assumptions on the penalty parameter and the objective function, the convergence of the proposed algorithm is obtained based on the Kurdyka–Łojasiewicz property. Moreover, we report some preliminary numerical results on involving matrix decomposition problem to demonstrate the feasibility and effectiveness of the proposed method.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02778-2