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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Vydáno v:Journal of optimization theory and applications Ročník 207; číslo 1; s. 17
Hlavní autoři: Zhao, Jing, Guo, Chenzheng, Qin, Xiaolong
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer Nature B.V 01.10.2025
Témata:
Algorithms
Constraints
Convex analysis
Lagrange multiplier
Multipliers
Optimization
ISSN:0022-3239, 1573-2878
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02778-2